CINXE.COM

<!DOCTYPE html> <html lang="en" dir="ltr"> <head>  <script async src="https://www.googletagmanager.com/gtag/js?id=G-P63WKM1TM1"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-P63WKM1TM1'); </script>  <script type="text/javascript" > (function(m,e,t,r,i,k,a){m[i]=m[i]||function(){(m[i].a=m[i].a||[]).push(arguments)}; m[i].l=1*new Date(); for (var j = 0; j < document.scripts.length; j++) {if (document.scripts[j].src === r) { return; }} k=e.createElement(t),a=e.getElementsByTagName(t)[0],k.async=1,k.src=r,a.parentNode.insertBefore(k,a)}) (window, document, "script", "https://mc.yandex.ru/metrika/tag.js", "ym"); ym(55165297, "init", { clickmap:false, trackLinks:true, accurateTrackBounce:true, webvisor:false }); </script> <noscript><div><img src="https://mc.yandex.ru/watch/55165297" style="position:absolute; left:-9999px;" alt="" /></div></noscript>    <title>Search results for: multi-objective fractional programming</title> <meta name="description" content="Search results for: multi-objective fractional programming"> <meta name="keywords" content="multi-objective fractional programming"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none navbar-toggler ml-auto" type="button" data-toggle="collapse" data-target="#navbarMenu" aria-controls="navbarMenu" aria-expanded="false" aria-label="Toggle navigation"> <span class="navbar-toggler-icon"></span> </button> <div class="w-100"> <div class="d-none d-lg-flex flex-row-reverse"> <form method="get" action="https://waset.org/search" class="form-inline my-2 my-lg-0"> <input class="form-control mr-sm-2" type="search" placeholder="Search Conferences" value="multi-objective fractional programming" name="q" aria-label="Search"> <button class="btn btn-light my-2 my-sm-0" type="submit"><i class="fas fa-search"></i></button> </form> </div> <div class="collapse navbar-collapse mt-1" id="navbarMenu"> <ul class="navbar-nav ml-auto align-items-center" id="mainNavMenu"> <li class="nav-item"> <a class="nav-link" href="https://waset.org/conferences" title="Conferences in 2024/2025/2026">Conferences</a> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/disciplines" title="Disciplines">Disciplines</a> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/committees" rel="nofollow">Committees</a> </li> <li class="nav-item dropdown"> <a class="nav-link dropdown-toggle" href="#" id="navbarDropdownPublications" role="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false"> Publications </a> <div class="dropdown-menu" aria-labelledby="navbarDropdownPublications"> <a class="dropdown-item" href="https://publications.waset.org/abstracts">Abstracts</a> <a class="dropdown-item" href="https://publications.waset.org">Periodicals</a> <a class="dropdown-item" href="https://publications.waset.org/archive">Archive</a> </div> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/page/support" title="Support">Support</a> </li> </ul> </div> </div> </nav> </div> </header> <main> <div class="container mt-4"> <div class="row"> <div class="col-md-9 mx-auto"> <form method="get" action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="multi-objective fractional programming"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 1173</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: multi-objective fractional programming</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1173</span> Duality in Multiobjective Nonlinear Programming under Generalized Second Order (F, b, φ, ρ, θ)− Univex Functions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Meraj%20Ali%20Khan">Meraj Ali Khan</a>, <a href="https://publications.waset.org/abstracts/search?q=Falleh%20R.%20Al-Solamy"> Falleh R. Al-Solamy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present paper, second order duality for multiobjective nonlinear programming are investigated under the second order generalized (F, b, φ, ρ, θ)− univex functions. The weak, strong and converse duality theorems are proved. Further, we also illustrated an example of (F, b, φ, ρ, θ)− univex functions. Results obtained in this paper extend some previously known results of multiobjective nonlinear programming in the literature. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=duality" title="duality">duality</a>, <a href="https://publications.waset.org/abstracts/search?q=multiobjective%20programming" title=" multiobjective programming"> multiobjective programming</a>, <a href="https://publications.waset.org/abstracts/search?q=univex%20functions" title=" univex functions"> univex functions</a>, <a href="https://publications.waset.org/abstracts/search?q=univex" title=" univex"> univex</a> </p> <a href="https://publications.waset.org/abstracts/4320/duality-in-multiobjective-nonlinear-programming-under-generalized-second-order-f-b-f-r-th-univex-functions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/4320.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">354</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1172</span> Finding Optimal Solutions to Management Problems with the use of Econometric and Multiobjective Programming</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Moradi%20Dalini">M. Moradi Dalini</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20R.%20Talebi"> M. R. Talebi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This research revolves around a technical method according to combines econometric and multiobjective programming to select and obtain optimal solutions to management problems. It is taken for a generation that; it is important to analyze which combination of values of the explanatory variables -in an econometric method- would point to the simultaneous achievement of the best values of the response variables. In this case, if a certain degree of conflict is viewed among the response variables, we suggest a multiobjective method in order to the results obtained from a regression analysis. In fact, with the use of a multiobjective method, we will have the best decision about the conflicting relationship between the response variables and the optimal solution. The combined multiobjective programming and econometrics benefit is an assessment of a balanced “optimal” situation among them because a find of information can hardly be extracted just by econometric techniques. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=econometrics" title="econometrics">econometrics</a>, <a href="https://publications.waset.org/abstracts/search?q=multiobjective%20optimization" title=" multiobjective optimization"> multiobjective optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=management%20problem" title=" management problem"> management problem</a>, <a href="https://publications.waset.org/abstracts/search?q=optimization" title=" optimization"> optimization</a> </p> <a href="https://publications.waset.org/abstracts/167999/finding-optimal-solutions-to-management-problems-with-the-use-of-econometric-and-multiobjective-programming" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/167999.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">82</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1171</span> A Fuzzy Programming Approach for Solving Intuitionistic Fuzzy Linear Fractional Programming Problem</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sujeet%20Kumar%20Singh">Sujeet Kumar Singh</a>, <a href="https://publications.waset.org/abstracts/search?q=Shiv%20Prasad%20Yadav"> Shiv Prasad Yadav</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper develops an approach for solving intuitionistic fuzzy linear fractional programming (IFLFP) problem where the cost of the objective function, the resources, and the technological coefficients are triangular intuitionistic fuzzy numbers. Here, the IFLFP problem is transformed into an equivalent crisp multi-objective linear fractional programming (MOLFP) problem. By using fuzzy mathematical programming approach the transformed MOLFP problem is reduced into a single objective linear programming (LP) problem. The proposed procedure is illustrated through a numerical example. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=triangular%20intuitionistic%20fuzzy%20number" title="triangular intuitionistic fuzzy number">triangular intuitionistic fuzzy number</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20programming%20problem" title=" linear programming problem"> linear programming problem</a>, <a href="https://publications.waset.org/abstracts/search?q=multi%20objective%20linear%20programming%20problem" title=" multi objective linear programming problem"> multi objective linear programming problem</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20mathematical%20programming" title=" fuzzy mathematical programming"> fuzzy mathematical programming</a>, <a href="https://publications.waset.org/abstracts/search?q=membership%20function" title=" membership function"> membership function</a> </p> <a href="https://publications.waset.org/abstracts/16411/a-fuzzy-programming-approach-for-solving-intuitionistic-fuzzy-linear-fractional-programming-problem" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/16411.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">566</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1170</span> Solution of Nonlinear Fractional Programming Problem with Bounded Parameters</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mrinal%20Jana">Mrinal Jana</a>, <a href="https://publications.waset.org/abstracts/search?q=Geetanjali%20Panda"> Geetanjali Panda</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper a methodology is developed to solve a nonlinear fractional programming problem in which the coefficients of the objective function and constraints are interval parameters. This model is transformed into a general optimization problem and relation between the original problem and the transformed problem is established. Finally the proposed methodology is illustrated through a numerical example. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20programming" title="fractional programming">fractional programming</a>, <a href="https://publications.waset.org/abstracts/search?q=interval%20valued%20function" title=" interval valued function"> interval valued function</a>, <a href="https://publications.waset.org/abstracts/search?q=interval%20inequalities" title=" interval inequalities"> interval inequalities</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20order%20relation" title=" partial order relation"> partial order relation</a> </p> <a href="https://publications.waset.org/abstracts/22261/solution-of-nonlinear-fractional-programming-problem-with-bounded-parameters" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/22261.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">519</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1169</span> Multiobjective Economic Dispatch Using Optimal Weighting Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mandeep%20Kaur">Mandeep Kaur</a>, <a href="https://publications.waset.org/abstracts/search?q=Fatehgarh%20Sahib"> Fatehgarh Sahib</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The purpose of economic load dispatch is to allocate the required load demand between the available generation units such that the cost of operation is minimized. It is an optimization problem to find the most economical schedule of the generating units while satisfying load demand and operational constraints. The multiobjective optimization problem in which the engineer’s goal is to maximize or minimize not a single objective function but several objective functions simultaneously. The purpose of multiobjective problems in the mathematical programming framework is to optimize the different objective functions. Many approaches and methods have been proposed in recent years to solve multiobjective optimization problems. Weighting method has been applied to convert multiobjective optimization problems into scalar optimization. MATLAB 7.10 has been used to write the code for the complete algorithm with the help of genetic algorithm (GA). The validity of the proposed method has been demonstrated on a three-unit power system. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=economic%20load%20dispatch" title="economic load dispatch">economic load dispatch</a>, <a href="https://publications.waset.org/abstracts/search?q=genetic%20algorithm" title=" genetic algorithm"> genetic algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=generating%20units" title=" generating units"> generating units</a>, <a href="https://publications.waset.org/abstracts/search?q=multiobjective%20optimization" title=" multiobjective optimization"> multiobjective optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=weighting%20method" title=" weighting method"> weighting method</a> </p> <a href="https://publications.waset.org/abstracts/117420/multiobjective-economic-dispatch-using-optimal-weighting-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/117420.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">150</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1168</span> Non-Differentiable Mond-Weir Type Symmetric Duality under Generalized Invexity</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jai%20Prakash%20Verma">Jai Prakash Verma</a>, <a href="https://publications.waset.org/abstracts/search?q=Khushboo%20Verma"> Khushboo Verma</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present paper, a pair of Mond-Weir type non-differentiable multiobjective second-order programming problems, involving two kernel functions, where each of the objective functions contains support function, is formulated. We prove weak, strong and converse duality theorem for the second-order symmetric dual programs under η-pseudoinvexity conditions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=non-differentiable%20multiobjective%20programming" title="non-differentiable multiobjective programming">non-differentiable multiobjective programming</a>, <a href="https://publications.waset.org/abstracts/search?q=second-order%20symmetric%20duality" title=" second-order symmetric duality"> second-order symmetric duality</a>, <a href="https://publications.waset.org/abstracts/search?q=efficiency" title=" efficiency"> efficiency</a>, <a href="https://publications.waset.org/abstracts/search?q=support%20function" title=" support function"> support function</a>, <a href="https://publications.waset.org/abstracts/search?q=eta-pseudoinvexity" title=" eta-pseudoinvexity"> eta-pseudoinvexity</a> </p> <a href="https://publications.waset.org/abstracts/57852/non-differentiable-mond-weir-type-symmetric-duality-under-generalized-invexity" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/57852.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">249</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1167</span> Interval Bilevel Linear Fractional Programming</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=F.%20Hamidi">F. Hamidi</a>, <a href="https://publications.waset.org/abstracts/search?q=N.%20Amiri"> N. Amiri</a>, <a href="https://publications.waset.org/abstracts/search?q=H.%20Mishmast%20Nehi"> H. Mishmast Nehi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Bilevel Programming (BP) model has been presented for a decision making process that consists of two decision makers in a hierarchical structure. In fact, BP is a model for a static two person game (the leader player in the upper level and the follower player in the lower level) wherein each player tries to optimize his/her personal objective function under dependent constraints; this game is sequential and non-cooperative. The decision making variables are divided between the two players and one’s choice affects the other’s beneﬁt and choices. In other words, BP consists of two nested optimization problems with two objective functions (upper and lower) where the constraint region of the upper level problem is implicitly determined by the lower level problem. In real cases, the coeﬃcients of an optimization problem may not be precise, i.e. they may be interval. In this paper we develop an algorithm for solving interval bilevel linear fractional programming problems. That is to say, bilevel problems in which both objective functions are linear fractional, the coefficients are interval and the common constraint region is a polyhedron. From the original problem, the best and the worst bilevel linear fractional problems have been derived and then, using the extended Charnes and Cooper transformation, each fractional problem can be reduced to a linear problem. Then we can ﬁnd the best and the worst optimal values of the leader objective function by two algorithms. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=best%20and%20worst%20optimal%20solutions" title="best and worst optimal solutions">best and worst optimal solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=bilevel%20programming" title=" bilevel programming"> bilevel programming</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional" title=" fractional"> fractional</a>, <a href="https://publications.waset.org/abstracts/search?q=interval%20coefficients" title=" interval coefficients"> interval coefficients</a> </p> <a href="https://publications.waset.org/abstracts/34778/interval-bilevel-linear-fractional-programming" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/34778.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">446</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1166</span> Examining the Performance of Three Multiobjective Evolutionary Algorithms Based on Benchmarking Problems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Konstantinos%20Metaxiotis">Konstantinos Metaxiotis</a>, <a href="https://publications.waset.org/abstracts/search?q=Konstantinos%20Liagkouras"> Konstantinos Liagkouras</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The objective of this study is to examine the performance of three well-known multiobjective evolutionary algorithms for solving optimization problems. The first algorithm is the Non-dominated Sorting Genetic Algorithm-II (NSGA-II), the second one is the Strength Pareto Evolutionary Algorithm 2 (SPEA-2), and the third one is the Multiobjective Evolutionary Algorithms based on decomposition (MOEA/D). The examined multiobjective algorithms are analyzed and tested on the ZDT set of test functions by three performance metrics. The results indicate that the NSGA-II performs better than the other two algorithms based on three performance metrics. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=MOEAs" title="MOEAs">MOEAs</a>, <a href="https://publications.waset.org/abstracts/search?q=multiobjective%20optimization" title=" multiobjective optimization"> multiobjective optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=ZDT%20test%20functions" title=" ZDT test functions"> ZDT test functions</a>, <a href="https://publications.waset.org/abstracts/search?q=evolutionary%20algorithms" title=" evolutionary algorithms"> evolutionary algorithms</a> </p> <a href="https://publications.waset.org/abstracts/65331/examining-the-performance-of-three-multiobjective-evolutionary-algorithms-based-on-benchmarking-problems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/65331.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">469</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1165</span> Interactive Solutions for the Multi-Objective Capacitated Transportation Problem with Mixed Constraints under Fuzziness</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Aquil%20Ahmed">Aquil Ahmed</a>, <a href="https://publications.waset.org/abstracts/search?q=Srikant%20Gupta"> Srikant Gupta</a>, <a href="https://publications.waset.org/abstracts/search?q=Irfan%20Ali"> Irfan Ali</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we study a multi-objective capacitated transportation problem (MOCTP) with mixed constraints. This paper is comprised of the modelling and optimisation of an MOCTP in a fuzzy environment in which some goals are fractional and some are linear. In real life application of the fuzzy goal programming (FGP) problem with multiple objectives, it is difficult for the decision maker(s) to determine the goal value of each objective precisely as the goal values are imprecise or uncertain. Also, we developed the concept of linearization of fractional goal for solving the MOCTP. In this paper, imprecision of the parameter is handled by the concept of fuzzy set theory by considering these parameters as a trapezoidal fuzzy number. α-cut approach is used to get the crisp value of the parameters. Numerical examples are used to illustrate the method for solving MOCTP. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=capacitated%20transportation%20problem" title="capacitated transportation problem">capacitated transportation problem</a>, <a href="https://publications.waset.org/abstracts/search?q=multi%20objective%20linear%20programming" title=" multi objective linear programming"> multi objective linear programming</a>, <a href="https://publications.waset.org/abstracts/search?q=multi-objective%20fractional%20programming" title=" multi-objective fractional programming"> multi-objective fractional programming</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20goal%20programming" title=" fuzzy goal programming"> fuzzy goal programming</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20sets" title=" fuzzy sets"> fuzzy sets</a>, <a href="https://publications.waset.org/abstracts/search?q=trapezoidal%20fuzzy%20number" title=" trapezoidal fuzzy number"> trapezoidal fuzzy number</a> </p> <a href="https://publications.waset.org/abstracts/77380/interactive-solutions-for-the-multi-objective-capacitated-transportation-problem-with-mixed-constraints-under-fuzziness" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/77380.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">434</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1164</span> Modified Fractional Curl Operator</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Rawhy%20Ismail">Rawhy Ismail </a> </p> <p class="card-text"><strong>Abstract:</strong></p> Applying fractional calculus in the field of electromagnetics shows significant results. The fractionalization of the conventional curl operator leads to having additional solutions to an electromagnetic problem. This work restudies the concept of the fractional curl operator considering fractional time derivatives in Maxwell’s curl equations. In that sense, a general scheme for the wave loss term is introduced and the degree of freedom of the system is affected through imposing the new fractional parameters. The conventional case is recovered by setting all fractional derivatives to unity. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=curl%20operator" title="curl operator">curl operator</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20calculus" title=" fractional calculus"> fractional calculus</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20curl%20operators" title=" fractional curl operators"> fractional curl operators</a>, <a href="https://publications.waset.org/abstracts/search?q=Maxwell%20equations" title=" Maxwell equations"> Maxwell equations</a> </p> <a href="https://publications.waset.org/abstracts/35772/modified-fractional-curl-operator" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/35772.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">487</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1163</span> Multi-Criteria Goal Programming Model for Sustainable Development of India </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Irfan%20Ali">Irfan Ali</a>, <a href="https://publications.waset.org/abstracts/search?q=Srikant%20Gupta"> Srikant Gupta</a>, <a href="https://publications.waset.org/abstracts/search?q=Aquil%20Ahmed"> Aquil Ahmed</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Every country needs a sustainable development (SD) for its economic growth by forming suitable policies and initiative programs for the development of different sectors of the country. This paper is comprised of modeling and optimization of different sectors of India that form a multi-criterion model. In this paper, we developed a fractional goal programming (FGP) model that helps in providing the efficient allocation of resources simultaneously by achieving the sustainable goals in gross domestic product (GDP), electricity consumption (EC) and greenhouse gasses (GHG) emission by the year 2030. Also, a weighted model of FGP is presented to obtain varying solution according to the priorities set by the policy maker for achieving future goals of GDP growth, EC, and GHG emission. The presented models provide a useful insight to the decision makers for implementing strategies in a different sector. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=sustainable%20and%20economic%20development" title="sustainable and economic development">sustainable and economic development</a>, <a href="https://publications.waset.org/abstracts/search?q=multi-objective%20fractional%20programming" title=" multi-objective fractional programming"> multi-objective fractional programming</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20goal%20programming" title=" fuzzy goal programming"> fuzzy goal programming</a>, <a href="https://publications.waset.org/abstracts/search?q=weighted%20fuzzy%20goal%20programming" title=" weighted fuzzy goal programming"> weighted fuzzy goal programming</a> </p> <a href="https://publications.waset.org/abstracts/77381/multi-criteria-goal-programming-model-for-sustainable-development-of-india" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/77381.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">223</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1162</span> Fractional Calculus into Structural Dynamics</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jorge%20Lopez">Jorge Lopez</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we introduce fractional calculus in order to study the dynamics of a damped multistory building with some symmetry. Initially we make a review of the dynamics of a free and damped multistory building. Then we introduce those concepts of fractional calculus that will be involved in our study. It has been noticed that fractional calculus provides models with less parameters than those based on classical calculus. In particular, a damped classical oscilator is more naturally described by using fractional derivatives. Accordingly, we model our multistory building as a set of coupled fractional oscillators and compare its dynamics with the results coming from traditional methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=coupled%20oscillators" title="coupled oscillators">coupled oscillators</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20calculus" title=" fractional calculus"> fractional calculus</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20oscillator" title=" fractional oscillator"> fractional oscillator</a>, <a href="https://publications.waset.org/abstracts/search?q=structural%20dynamics" title=" structural dynamics"> structural dynamics</a> </p> <a href="https://publications.waset.org/abstracts/124822/fractional-calculus-into-structural-dynamics" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/124822.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">242</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1161</span> Fractional Order Differentiator Using Chebyshev Polynomials</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Koushlendra%20Kumar%20Singh">Koushlendra Kumar Singh</a>, <a href="https://publications.waset.org/abstracts/search?q=Manish%20Kumar%20Bajpai"> Manish Kumar Bajpai</a>, <a href="https://publications.waset.org/abstracts/search?q=Rajesh%20Kumar%20Pandey"> Rajesh Kumar Pandey</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A discrete time fractional orderdifferentiator has been modeled for estimating the fractional order derivatives of contaminated signal. The proposed approach is based on Chebyshev’s polynomials. We use the Riemann-Liouville fractional order derivative definition for designing the fractional order SG differentiator. In first step we calculate the window weight corresponding to the required fractional order. Then signal is convoluted with this calculated window’s weight for finding the fractional order derivatives of signals. Several signals are considered for evaluating the accuracy of the proposed method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20order%20derivative" title="fractional order derivative">fractional order derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=chebyshev%0D%0Apolynomials" title=" chebyshev polynomials"> chebyshev polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=signals" title=" signals"> signals</a>, <a href="https://publications.waset.org/abstracts/search?q=S-G%20differentiator" title=" S-G differentiator"> S-G differentiator</a> </p> <a href="https://publications.waset.org/abstracts/21346/fractional-order-differentiator-using-chebyshev-polynomials" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/21346.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">648</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1160</span> Fractional Euler Method and Finite Difference Formula Using Conformable Fractional Derivative</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ramzi%20B.%20Albadarneh">Ramzi B. Albadarneh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we use the new definition of fractional derivative called conformable fractional derivative to derive some finite difference formulas and its error terms which are used to solve fractional differential equations and fractional partial differential equations, also to derive fractional Euler method and its error terms which can be applied to solve fractional differential equations. To provide the contribution of our work some applications on finite difference formulas and Euler Method are given. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conformable%20fractional%20derivative" title="conformable fractional derivative">conformable fractional derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20difference%20formula" title=" finite difference formula"> finite difference formula</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20derivative" title=" fractional derivative"> fractional derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20difference%20formula" title=" finite difference formula"> finite difference formula</a> </p> <a href="https://publications.waset.org/abstracts/37072/fractional-euler-method-and-finite-difference-formula-using-conformable-fractional-derivative" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/37072.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">439</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1159</span> Protein Tertiary Structure Prediction by a Multiobjective Optimization and Neural Network Approach</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Alexandre%20Barbosa%20de%20Almeida">Alexandre Barbosa de Almeida</a>, <a href="https://publications.waset.org/abstracts/search?q=Telma%20Woerle%20de%20Lima%20Soares"> Telma Woerle de Lima Soares</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Protein structure prediction is a challenging task in the bioinformatics field. The biological function of all proteins majorly relies on the shape of their three-dimensional conformational structure, but less than 1% of all known proteins in the world have their structure solved. This work proposes a deep learning model to address this problem, attempting to predict some aspects of the protein conformations. Throughout a process of multiobjective dominance, a recurrent neural network was trained to abstract the particular bias of each individual multiobjective algorithm, generating a heuristic that could be useful to predict some of the relevant aspects of the three-dimensional conformation process formation, known as protein folding. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ab%20initio%20heuristic%20modeling" title="Ab initio heuristic modeling">Ab initio heuristic modeling</a>, <a href="https://publications.waset.org/abstracts/search?q=multiobjective%20optimization" title=" multiobjective optimization"> multiobjective optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=protein%20structure%20prediction" title=" protein structure prediction"> protein structure prediction</a>, <a href="https://publications.waset.org/abstracts/search?q=recurrent%20neural%20network" title=" recurrent neural network"> recurrent neural network</a> </p> <a href="https://publications.waset.org/abstracts/141565/protein-tertiary-structure-prediction-by-a-multiobjective-optimization-and-neural-network-approach" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/141565.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">205</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1158</span> Caputo-Type Fuzzy Fractional Riccati Differential Equations with Fuzzy Initial Conditions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Trilok%20Mathur">Trilok Mathur</a>, <a href="https://publications.waset.org/abstracts/search?q=Shivi%20Agarwal"> Shivi Agarwal</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper deals with the solutions of fuzzy-fractional-order Riccati equations under Caputo-type fuzzy fractional derivatives. The Caputo-type fuzzy fractional derivatives are defined based on Hukuhura difference and strongly generalized fuzzy differentiability. The Laplace-Adomian-Pade method is used for solving fractional Riccati-type initial value differential equations of fractional order. Moreover, we also displayed some examples to illustrate our methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Caputo-type%20fuzzy%20fractional%20derivative" title="Caputo-type fuzzy fractional derivative">Caputo-type fuzzy fractional derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=Fractional%20Riccati%20differential%20equations" title=" Fractional Riccati differential equations"> Fractional Riccati differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Laplace-Adomian-Pade%20method" title=" Laplace-Adomian-Pade method"> Laplace-Adomian-Pade method</a>, <a href="https://publications.waset.org/abstracts/search?q=Mittag%20Leffler%20function" title=" Mittag Leffler function"> Mittag Leffler function</a> </p> <a href="https://publications.waset.org/abstracts/51080/caputo-type-fuzzy-fractional-riccati-differential-equations-with-fuzzy-initial-conditions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/51080.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">395</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1157</span> Derivation of Fractional Black-Scholes Equations Driven by Fractional G-Brownian Motion and Their Application in European Option Pricing</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Changhong%20Guo">Changhong Guo</a>, <a href="https://publications.waset.org/abstracts/search?q=Shaomei%20Fang"> Shaomei Fang</a>, <a href="https://publications.waset.org/abstracts/search?q=Yong%20He"> Yong He</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, fractional Black-Scholes models for the European option pricing were established based on the fractional G-Brownian motion (fGBm), which generalizes the concepts of the classical Brownian motion, fractional Brownian motion and the G-Brownian motion, and that can be used to be a tool for considering the long range dependence and uncertain volatility for the financial markets simultaneously. A generalized fractional Black-Scholes equation (FBSE) was derived by using the Taylor’s series of fractional order and the theory of absence of arbitrage. Finally, some explicit option pricing formulas for the European call option and put option under the FBSE were also solved, which extended the classical option pricing formulas given by F. Black and M. Scholes. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=European%20option%20pricing" title="European option pricing">European option pricing</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20Black-Scholes%20equations" title=" fractional Black-Scholes equations"> fractional Black-Scholes equations</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20g-Brownian%20motion" title=" fractional g-Brownian motion"> fractional g-Brownian motion</a>, <a href="https://publications.waset.org/abstracts/search?q=Taylor%27s%20series%20of%20fractional%20order" title=" Taylor's series of fractional order"> Taylor's series of fractional order</a>, <a href="https://publications.waset.org/abstracts/search?q=uncertain%20volatility" title=" uncertain volatility"> uncertain volatility</a> </p> <a href="https://publications.waset.org/abstracts/127107/derivation-of-fractional-black-scholes-equations-driven-by-fractional-g-brownian-motion-and-their-application-in-european-option-pricing" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/127107.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">163</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1156</span> Reduced Differential Transform Methods for Solving the Fractional Diffusion Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yildiray%20Keskin">Yildiray Keskin</a>, <a href="https://publications.waset.org/abstracts/search?q=Omer%20Acan"> Omer Acan</a>, <a href="https://publications.waset.org/abstracts/search?q=Murat%20Akkus"> Murat Akkus</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the solution of fractional diffusion equations is presented by means of the reduced differential transform method. Fractional partial differential equations have special importance in engineering and sciences. Application of reduced differential transform method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. The numerical results show that the approach is easy to implement and accurate when applied to fractional diffusion equations. The method introduces a promising tool for solving many fractional partial differential equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20diffusion%20equations" title="fractional diffusion equations">fractional diffusion equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Caputo%20fractional%20derivative" title=" Caputo fractional derivative"> Caputo fractional derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=reduced%20differential%20transform%20method" title=" reduced differential transform method"> reduced differential transform method</a>, <a href="https://publications.waset.org/abstracts/search?q=partial" title=" partial"> partial</a> </p> <a href="https://publications.waset.org/abstracts/17526/reduced-differential-transform-methods-for-solving-the-fractional-diffusion-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17526.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">525</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1155</span> Relation between Roots and Tangent Lines of Function in Fractional Dimensions: A Method for Optimization Problems </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ali%20Dorostkar">Ali Dorostkar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a basic schematic of fractional dimensional optimization problem is presented. As will be shown, a method is performed based on a relation between roots and tangent lines of function in fractional dimensions for an arbitrary initial point. It is shown that for each polynomial function with order N at least N tangent lines must be existed in fractional dimensions of 0 < α < N+1 which pass exactly through the all roots of the proposed function. Geometrical analysis of tangent lines in fractional dimensions is also presented to clarify more intuitively the proposed method. Results show that with an appropriate selection of fractional dimensions, we can directly find the roots. Method is presented for giving a different direction of optimization problems by the use of fractional dimensions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=tangent%20line" title="tangent line">tangent line</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20dimension" title=" fractional dimension"> fractional dimension</a>, <a href="https://publications.waset.org/abstracts/search?q=root" title=" root"> root</a>, <a href="https://publications.waset.org/abstracts/search?q=optimization%20problem" title=" optimization problem"> optimization problem</a> </p> <a href="https://publications.waset.org/abstracts/94257/relation-between-roots-and-tangent-lines-of-function-in-fractional-dimensions-a-method-for-optimization-problems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/94257.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">192</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1154</span> An Enhanced Particle Swarm Optimization Algorithm for Multiobjective Problems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Houda%20Abadlia">Houda Abadlia</a>, <a href="https://publications.waset.org/abstracts/search?q=Nadia%20Smairi"> Nadia Smairi</a>, <a href="https://publications.waset.org/abstracts/search?q=Khaled%20Ghedira"> Khaled Ghedira</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Multiobjective Particle Swarm Optimization (MOPSO) has shown an effective performance for solving test functions and real-world optimization problems. However, this method has a premature convergence problem, which may lead to lack of diversity. In order to improve its performance, this paper presents a hybrid approach which embedded the MOPSO into the island model and integrated a local search technique, Variable Neighborhood Search, to enhance the diversity into the swarm. Experiments on two series of test functions have shown the effectiveness of the proposed approach. A comparison with other evolutionary algorithms shows that the proposed approach presented a good performance in solving multiobjective optimization problems. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=particle%20swarm%20optimization" title="particle swarm optimization">particle swarm optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=migration" title=" migration"> migration</a>, <a href="https://publications.waset.org/abstracts/search?q=variable%20neighborhood%20search" title=" variable neighborhood search"> variable neighborhood search</a>, <a href="https://publications.waset.org/abstracts/search?q=multiobjective%20optimization" title=" multiobjective optimization"> multiobjective optimization</a> </p> <a href="https://publications.waset.org/abstracts/99544/an-enhanced-particle-swarm-optimization-algorithm-for-multiobjective-problems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/99544.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">167</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1153</span> Design Fractional-Order Terminal Sliding Mode Control for Synchronization of a Class of Fractional-Order Chaotic Systems with Uncertainty and External Disturbances</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shabnam%20Pashaei">Shabnam Pashaei</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohammadali%20Badamchizadeh"> Mohammadali Badamchizadeh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents a new fractional-order terminal sliding mode control for synchronization of two different fractional-order chaotic systems with uncertainty and external disturbances. A fractional-order integral type nonlinear switching surface is presented. Then, using the Lyapunov stability theory and sliding mode theory, a fractional-order control law is designed to synchronize two different fractional-order chaotic systems. Finally, a simulation example is presented to illustrate the performance and applicability of the proposed method. Based on numerical results, the proposed controller ensures that the states of the controlled fractional-order chaotic response system are asymptotically synchronized with the states of the drive system. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=terminal%20sliding%20mode%20control" title="terminal sliding mode control">terminal sliding mode control</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional-order%20calculus" title=" fractional-order calculus"> fractional-order calculus</a>, <a href="https://publications.waset.org/abstracts/search?q=chaotic%20systems" title=" chaotic systems"> chaotic systems</a>, <a href="https://publications.waset.org/abstracts/search?q=synchronization" title=" synchronization"> synchronization</a> </p> <a href="https://publications.waset.org/abstracts/67276/design-fractional-order-terminal-sliding-mode-control-for-synchronization-of-a-class-of-fractional-order-chaotic-systems-with-uncertainty-and-external-disturbances" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/67276.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">409</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1152</span> Lyapunov Type Inequalities for Fractional Impulsive Hamiltonian Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kazem%20Ghanbari">Kazem Ghanbari</a>, <a href="https://publications.waset.org/abstracts/search?q=Yousef%20Gholami"> Yousef Gholami</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper deals with study about fractional order impulsive Hamiltonian systems and fractional impulsive Sturm-Liouville type problems derived from these systems. The main purpose of this paper devotes to obtain so called Lyapunov type inequalities for mentioned problems. Also, in view point on applicability of obtained inequalities, some qualitative properties such as stability, disconjugacy, nonexistence and oscillatory behaviour of fractional Hamiltonian systems and fractional Sturm-Liouville type problems under impulsive conditions will be derived. At the end, we want to point out that for studying fractional order Hamiltonian systems, we will apply recently introduced fractional Conformable operators. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20derivatives%20and%20integrals" title="fractional derivatives and integrals">fractional derivatives and integrals</a>, <a href="https://publications.waset.org/abstracts/search?q=Hamiltonian%20system" title=" Hamiltonian system"> Hamiltonian system</a>, <a href="https://publications.waset.org/abstracts/search?q=Lyapunov-type%20inequalities" title=" Lyapunov-type inequalities"> Lyapunov-type inequalities</a>, <a href="https://publications.waset.org/abstracts/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/abstracts/search?q=disconjugacy" title=" disconjugacy"> disconjugacy</a> </p> <a href="https://publications.waset.org/abstracts/48806/lyapunov-type-inequalities-for-fractional-impulsive-hamiltonian-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/48806.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">354</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1151</span> Solutions of Fractional Reaction-Diffusion Equations Used to Model the Growth and Spreading of Biological Species</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kamel%20Al-Khaled">Kamel Al-Khaled</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Reaction-diffusion equations are commonly used in population biology to model the spread of biological species. In this paper, we propose a fractional reaction-diffusion equation, where the classical second derivative diffusion term is replaced by a fractional derivative of order less than two. Based on the symbolic computation system Mathematica, Adomian decomposition method, developed for fractional differential equations, is directly extended to derive explicit and numerical solutions of space fractional reaction-diffusion equations. The fractional derivative is described in the Caputo sense. Finally, the recent appearance of fractional reaction-diffusion equations as models in some ﬁelds such as cell biology, chemistry, physics, and ﬁnance, makes it necessary to apply the results reported here to some numerical examples. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20partial%20differential%20equations" title="fractional partial differential equations">fractional partial differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=reaction-di%EF%AC%80usion%20equations" title=" reaction-diﬀusion equations"> reaction-diﬀusion equations</a>, <a href="https://publications.waset.org/abstracts/search?q=adomian%20decomposition" title=" adomian decomposition"> adomian decomposition</a>, <a href="https://publications.waset.org/abstracts/search?q=biological%20species" title=" biological species"> biological species</a> </p> <a href="https://publications.waset.org/abstracts/55994/solutions-of-fractional-reaction-diffusion-equations-used-to-model-the-growth-and-spreading-of-biological-species" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/55994.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">375</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1150</span> Multi-Period Supply Chain Design under Uncertainty</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Amir%20Azaron">Amir Azaron</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this research, a stochastic programming approach is developed for designing supply chains with uncertain parameters. Demands and selling prices of products at markets are considered as the uncertain parameters. The proposed mathematical model will be multi-period two-stage stochastic programming, which takes into account the selection of retailer sites, suppliers, production levels, inventory levels, transportation modes to be used for shipping goods, and shipping quantities among the entities of the supply chain network. The objective function is to maximize the chain’s net present value. In order to maximize the chain’s NPV, the sum of first-stage investment costs on retailers, and the expected second-stage processing, inventory-holding and transportation costs should be kept as low as possible over multiple periods. The effects of supply uncertainty where suppliers are unreliable will also be investigated on the efficiency of the supply chain. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=supply%20chain%20management" title="supply chain management">supply chain management</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20programming" title=" stochastic programming"> stochastic programming</a>, <a href="https://publications.waset.org/abstracts/search?q=multiobjective%20programming" title=" multiobjective programming"> multiobjective programming</a>, <a href="https://publications.waset.org/abstracts/search?q=inventory%20control" title=" inventory control"> inventory control</a> </p> <a href="https://publications.waset.org/abstracts/66297/multi-period-supply-chain-design-under-uncertainty" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/66297.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">295</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1149</span> Weak Solutions Of Stochastic Fractional Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Lev%20Idels">Lev Idels</a>, <a href="https://publications.waset.org/abstracts/search?q=Arcady%20Ponosov"> Arcady Ponosov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Stochastic fractional differential equations have recently attracted considerable attention, as they have been used to model real-world processes, which are subject to natural memory effects and measurement uncertainties. Compared to conventional hereditary differential equations, one of the advantages of fractional differential equations is related to more realistic geometric properties of their trajectories that do not intersect in the phase space. In this report, a Peano-like existence theorem for nonlinear stochastic fractional differential equations is proven under very general hypotheses. Several specific classes of equations are checked to satisfy these hypotheses, including delay equations driven by the fractional Brownian motion, stochastic fractional neutral equations and many others. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=delay%20equations" title="delay equations">delay equations</a>, <a href="https://publications.waset.org/abstracts/search?q=operator%20methods" title=" operator methods"> operator methods</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20noise" title=" stochastic noise"> stochastic noise</a>, <a href="https://publications.waset.org/abstracts/search?q=weak%20solutions" title=" weak solutions"> weak solutions</a> </p> <a href="https://publications.waset.org/abstracts/146592/weak-solutions-of-stochastic-fractional-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/146592.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">209</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1148</span> Application of Fractional Model Predictive Control to Thermal System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Aymen%20Rhouma">Aymen Rhouma</a>, <a href="https://publications.waset.org/abstracts/search?q=Khaled%20Hcheichi"> Khaled Hcheichi</a>, <a href="https://publications.waset.org/abstracts/search?q=Sami%20Hafsi"> Sami Hafsi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The article presents an application of Fractional Model Predictive Control (FMPC) to a fractional order thermal system using Controlled Auto Regressive Integrated Moving Average (CARIMA) model obtained by discretization of a continuous fractional differential equation. Moreover, the output deviation approach is exploited to design the K -step ahead output predictor, and the corresponding control law is obtained by solving a quadratic cost function. Experiment results onto a thermal system are presented to emphasize the performances and the effectiveness of the proposed predictive controller<em>.</em> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20model%20predictive%20control" title="fractional model predictive control">fractional model predictive control</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20order%20systems" title=" fractional order systems"> fractional order systems</a>, <a href="https://publications.waset.org/abstracts/search?q=thermal%20system" title=" thermal system"> thermal system</a>, <a href="https://publications.waset.org/abstracts/search?q=predictive%20control" title=" predictive control"> predictive control</a> </p> <a href="https://publications.waset.org/abstracts/66187/application-of-fractional-model-predictive-control-to-thermal-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/66187.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">411</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1147</span> A New Study on Mathematical Modelling of COVID-19 with Caputo Fractional Derivative</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sadia%20Arshad">Sadia Arshad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The new coronavirus disease or COVID-19 still poses an alarming situation around the world. Modeling based on the derivative of fractional order is relatively important to capture real-world problems and to analyze the realistic situation of the proposed model. Weproposed a mathematical model for the investigation of COVID-19 dynamics in a generalized fractional framework. The new model is formulated in the Caputo sense and employs a nonlinear time-varying transmission rate. The existence and uniqueness solutions of the fractional order derivative have been studied using the fixed-point theory. The associated dynamical behaviors are discussed in terms of equilibrium, stability, and basic reproduction number. For the purpose of numerical implementation, an effcient approximation scheme is also employed to solve the fractional COVID-19 model. Numerical simulations are reported for various fractional orders, and simulation results are compared with a real case of COVID-19 pandemic. According to the comparative results with real data, we find the best value of fractional orderand justify the use of the fractional concept in the mathematical modelling, for the new fractional modelsimulates the reality more accurately than the other classical frameworks. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20calculus" title="fractional calculus">fractional calculus</a>, <a href="https://publications.waset.org/abstracts/search?q=modeling" title=" modeling"> modeling</a>, <a href="https://publications.waset.org/abstracts/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20solution" title=" numerical solution"> numerical solution</a> </p> <a href="https://publications.waset.org/abstracts/151862/a-new-study-on-mathematical-modelling-of-covid-19-with-caputo-fractional-derivative" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/151862.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">111</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1146</span> Oil Displacement by Water in Hauterivian Sandstone Reservoir of Kashkari Oil Field</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20J.%20Nazari">A. J. Nazari</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Honma"> S. Honma</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper evaluates oil displacement by water in Hauterivian sandstone reservoir of Kashkari oil field in North of Afghanistan. The core samples of this oil field were taken out from well No-21<sup>st</sup>, and the relative permeability and fractional flow are analyzed. Steady state flow laboratory experiments are performed to empirically obtain the fractional flow curves and relative permeability in different water saturation ratio. The relative permeability represents the simultaneous flow behavior in the reservoir. The fractional flow approach describes the individual phases as fractional of the total flow. The fractional flow curve interprets oil displacement by water, and from the tangent of fractional flow curve can find out the average saturation behind the water front flow saturation. Therefore, relative permeability and fractional flow curves are suitable for describing the displacement of oil by water in a petroleum reservoir. The effects of irreducible water saturation, residual oil saturation on the displaceable amount of oil are investigated through Buckley-Leveret analysis. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20flow" title="fractional flow">fractional flow</a>, <a href="https://publications.waset.org/abstracts/search?q=oil%20displacement" title=" oil displacement"> oil displacement</a>, <a href="https://publications.waset.org/abstracts/search?q=relative%20permeability" title=" relative permeability"> relative permeability</a>, <a href="https://publications.waset.org/abstracts/search?q=simultaneously%20flow" title=" simultaneously flow"> simultaneously flow</a> </p> <a href="https://publications.waset.org/abstracts/59190/oil-displacement-by-water-in-hauterivian-sandstone-reservoir-of-kashkari-oil-field" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/59190.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">392</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1145</span> Mixed Sub-Fractional Brownian Motion</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mounir%20Zili">Mounir Zili</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We will introduce a new extension of the Brownian motion, that could serve to get a good model of many natural phenomena. It is a linear combination of a finite number of sub-fractional Brownian motions; that is why we will call it the mixed sub-fractional Brownian motion. We will present some basic properties of this process. Among others, we will check that our process is non-Markovian and that it has non-stationary increments. We will also give the conditions under which it is a semimartingale. Finally, the main features of its sample paths will be specified. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=mixed%20Gaussian%20processes" title="mixed Gaussian processes">mixed Gaussian processes</a>, <a href="https://publications.waset.org/abstracts/search?q=Sub-fractional%20Brownian%20motion" title=" Sub-fractional Brownian motion"> Sub-fractional Brownian motion</a>, <a href="https://publications.waset.org/abstracts/search?q=sample%20paths" title=" sample paths"> sample paths</a> </p> <a href="https://publications.waset.org/abstracts/32479/mixed-sub-fractional-brownian-motion" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/32479.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">488</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1144</span> Multiobjective Optimization of a Pharmaceutical Formulation Using Regression Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=J.%20Satya%20Eswari">J. Satya Eswari</a>, <a href="https://publications.waset.org/abstracts/search?q=Ch.%20Venkateswarlu"> Ch. Venkateswarlu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The formulation of a commercial pharmaceutical product involves several composition factors and response characteristics. When the formulation requires to satisfy multiple response characteristics which are conflicting, an optimal solution requires the need for an efficient multiobjective optimization technique. In this work, a regression is combined with a non-dominated sorting differential evolution (NSDE) involving Naïve & Slow and ε constraint techniques to derive different multiobjective optimization strategies, which are then evaluated by means of a trapidil pharmaceutical formulation. The analysis of the results show the effectiveness of the strategy that combines the regression model and NSDE with the integration of both Naïve & Slow and ε constraint techniques for Pareto optimization of trapidil formulation. With this strategy, the optimal formulation at pH=6.8 is obtained with the decision variables of micro crystalline cellulose, hydroxypropyl methylcellulose and compression pressure. The corresponding response characteristics of rate constant and release order are also noted down. The comparison of these results with the experimental data and with those of other multiple regression model based multiobjective evolutionary optimization strategies signify the better performance for optimal trapidil formulation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=pharmaceutical%20formulation" title="pharmaceutical formulation">pharmaceutical formulation</a>, <a href="https://publications.waset.org/abstracts/search?q=multiple%20regression%20model" title=" multiple regression model"> multiple regression model</a>, <a href="https://publications.waset.org/abstracts/search?q=response%20surface%20method" title=" response surface method"> response surface method</a>, <a href="https://publications.waset.org/abstracts/search?q=radial%20basis%20function%20network" title=" radial basis function network"> radial basis function network</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20evolution" title=" differential evolution"> differential evolution</a>, <a href="https://publications.waset.org/abstracts/search?q=multiobjective%20optimization" title=" multiobjective optimization"> multiobjective optimization</a> </p> <a href="https://publications.waset.org/abstracts/62859/multiobjective-optimization-of-a-pharmaceutical-formulation-using-regression-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/62859.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">409</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multi-objective%20fractional%20programming&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multi-objective%20fractional%20programming&page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multi-objective%20fractional%20programming&page=4">4</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multi-objective%20fractional%20programming&page=5">5</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multi-objective%20fractional%20programming&page=6">6</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multi-objective%20fractional%20programming&page=7">7</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multi-objective%20fractional%20programming&page=8">8</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multi-objective%20fractional%20programming&page=9">9</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multi-objective%20fractional%20programming&page=10">10</a></li> <li class="page-item disabled"><span class="page-link">...</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multi-objective%20fractional%20programming&page=39">39</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multi-objective%20fractional%20programming&page=40">40</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multi-objective%20fractional%20programming&page=2" rel="next">&rsaquo;</a></li> </ul> </div> </main> <footer> <div id="infolinks" class="pt-3 pb-2"> <div class="container"> <div style="background-color:#f5f5f5;" class="p-3"> <div class="row"> <div class="col-md-2"> <ul class="list-unstyled"> About <li><a href="https://waset.org/page/support">About Us</a></li> <li><a href="https://waset.org/page/support#legal-information">Legal</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/WASET-16th-foundational-anniversary.pdf">WASET celebrates its 16th foundational anniversary</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Account <li><a href="https://waset.org/profile">My Account</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Explore <li><a href="https://waset.org/disciplines">Disciplines</a></li> <li><a href="https://waset.org/conferences">Conferences</a></li> <li><a href="https://waset.org/conference-programs">Conference Program</a></li> <li><a href="https://waset.org/committees">Committees</a></li> <li><a href="https://publications.waset.org">Publications</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Research <li><a href="https://publications.waset.org/abstracts">Abstracts</a></li> <li><a href="https://publications.waset.org">Periodicals</a></li> <li><a href="https://publications.waset.org/archive">Archive</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Open Science <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Science-Philosophy.pdf">Open Science Philosophy</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Science-Award.pdf">Open Science Award</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Society-Open-Science-and-Open-Innovation.pdf">Open Innovation</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Postdoctoral-Fellowship-Award.pdf">Postdoctoral Fellowship Award</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Scholarly-Research-Review.pdf">Scholarly Research Review</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Support <li><a href="https://waset.org/page/support">Support</a></li> <li><a href="https://waset.org/profile/messages/create">Contact Us</a></li> <li><a href="https://waset.org/profile/messages/create">Report Abuse</a></li> </ul> </div> </div> </div> </div> </div> <div class="container text-center"> <hr style="margin-top:0;margin-bottom:.3rem;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" class="text-muted small">Creative Commons Attribution 4.0 International License</a> <div id="copy" class="mt-2">© 2024 World Academy of Science, Engineering and Technology</div> </div> </footer> <a href="javascript:" id="return-to-top"><i class="fas fa-arrow-up"></i></a> <div class="modal" id="modal-template"> <div class="modal-dialog"> <div class="modal-content"> <div class="row m-0 mt-1"> <div class="col-md-12"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> </div> </div> <div class="modal-body"></div> </div> </div> </div> <script src="https://cdn.waset.org/static/plugins/jquery-3.3.1.min.js"></script> <script src="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.waset.org/static/js/site.js?v=150220211556"></script> <script> jQuery(document).ready(function() { /*jQuery.get("https://publications.waset.org/xhr/user-menu", function (response) { jQuery('#mainNavMenu').append(response); });*/ jQuery.get({ url: "https://publications.waset.org/xhr/user-menu", cache: false }).then(function(response){ jQuery('#mainNavMenu').append(response); }); }); </script> </body> </html>