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derivatives and integrals</title> <meta name="description" content="Search results for: fractional derivatives and integrals"> <meta name="keywords" content="fractional derivatives and integrals"> <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 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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="fractional derivatives and integrals"> <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> 823</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: fractional derivatives and integrals</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">823</span> Hermite–Hadamard Type Integral Inequalities Involving k–Riemann–Liouville Fractional Integrals and Their Applications</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Artion%20Kashuri">Artion Kashuri</a>, <a href="https://publications.waset.org/abstracts/search?q=Rozana%20Liko"> Rozana Liko</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, some generalization integral inequalities of Hermite–Hadamard type for functions whose derivatives are s–convex in modulus are given by using k–fractional integrals. Some applications to special means are obtained as well. Some known versions are recovered as special cases from our results. We note that our inequalities can be viewed as new refinements of the previous results. Finally, our results have a deep connection with various fractional integral operators and interested readers can find new interesting results using our idea and technique as well. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hermite-Hadamard%27s%20inequalities" title="Hermite-Hadamard's inequalities">Hermite-Hadamard's inequalities</a>, <a href="https://publications.waset.org/abstracts/search?q=H%C3%B6lder%27s%20inequality" title=" Hölder's inequality"> Hölder's inequality</a>, <a href="https://publications.waset.org/abstracts/search?q=k-Riemann-Liouville%20fractional%20integral" title=" k-Riemann-Liouville fractional integral"> k-Riemann-Liouville fractional integral</a>, <a href="https://publications.waset.org/abstracts/search?q=special%20means" title=" special means"> special means</a> </p> <a href="https://publications.waset.org/abstracts/127761/hermite-hadamard-type-integral-inequalities-involving-k-riemann-liouville-fractional-integrals-and-their-applications" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/127761.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">128</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">822</span> Robust Fractional Order Controllers for Minimum and Non-Minimum Phase Systems – Studies on Design and Development</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Anand%20Kishore%20Kola">Anand Kishore Kola</a>, <a href="https://publications.waset.org/abstracts/search?q=G.%20Uday%20Bhaskar%20Babu"> G. Uday Bhaskar Babu</a>, <a href="https://publications.waset.org/abstracts/search?q=Kotturi%20Ajay%20Kumar"> Kotturi Ajay Kumar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The modern dynamic systems used in industries are complex in nature and hence the fractional order controllers have been contemplated as a fresh approach to control system design that takes the complexity into account. Traditional integer order controllers use integer derivatives and integrals to control systems, whereas fractional order controllers use fractional derivatives and integrals to regulate memory and non-local behavior. This study provides a method based on the maximumsensitivity (Ms) methodology to discover all resilient fractional filter Internal Model Control - proportional integral derivative (IMC-PID) controllers that stabilize the closed-loop system and deliver the highest performance for a time delay system with a Smith predictor configuration. Additionally, it helps to enhance the range of PID controllers that are used to stabilize the system. This study also evaluates the effectiveness of the suggested controller approach for minimum phase system in comparison to those currently in use which are based on Integral of Absolute Error (IAE) and Total Variation (TV). <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=modern%20dynamic%20systems" title="modern dynamic systems">modern dynamic systems</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20order%20controllers" title=" fractional order controllers"> fractional order controllers</a>, <a href="https://publications.waset.org/abstracts/search?q=maximum-sensitivity" title=" maximum-sensitivity"> maximum-sensitivity</a>, <a href="https://publications.waset.org/abstracts/search?q=IMC-PID%20controllers" title=" IMC-PID controllers"> IMC-PID controllers</a>, <a href="https://publications.waset.org/abstracts/search?q=Smith%20predictor" title=" Smith predictor"> Smith predictor</a>, <a href="https://publications.waset.org/abstracts/search?q=IAE%20and%20TV" title=" IAE and TV"> IAE and TV</a> </p> <a href="https://publications.waset.org/abstracts/181141/robust-fractional-order-controllers-for-minimum-and-non-minimum-phase-systems-studies-on-design-and-development" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/181141.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">65</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">821</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">820</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">356</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">819</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">818</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">817</span> On Boundary Value Problems of Fractional Differential Equations Involving Stieltjes Derivatives</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Baghdad%20Said">Baghdad Said</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Differential equations of fractional order have proved to be important tools to describe many physical phenomena and have been used in diverse fields such as engineering, mathematics as well as other applied sciences. On the other hand, the theory of differential equations involving the Stieltjes derivative (SD) with respect to a non-decreasing function is a new class of differential equations and has many applications as a unified framework for dynamic equations on time scales and differential equations with impulses at fixed times. The aim of this paper is to investigate the existence, uniqueness, and generalized Ulam-Hyers-Rassias stability (UHRS) of solutions for a boundary value problem of sequential fractional differential equations (SFDE) containing (SD). This study is based on the technique of noncompactness measures (MNCs) combined with Monch-Krasnoselski fixed point theorems (FPT), and the results are proven in an appropriate Banach space under sufficient hypotheses. We also give an illustrative example. In this work, we introduced a class of (SFDE) and the results are obtained under a few hypotheses. Future directions connected to this work could focus on another problem with different types of fractional integrals and derivatives, and the (SD) will be assumed under a more general hypothesis in more general functional spaces. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=SFDE" title="SFDE">SFDE</a>, <a href="https://publications.waset.org/abstracts/search?q=SD" title=" SD"> SD</a>, <a href="https://publications.waset.org/abstracts/search?q=UHRS" title=" UHRS"> UHRS</a>, <a href="https://publications.waset.org/abstracts/search?q=MNCs" title=" MNCs"> MNCs</a>, <a href="https://publications.waset.org/abstracts/search?q=FPT" title=" FPT"> FPT</a> </p> <a href="https://publications.waset.org/abstracts/187408/on-boundary-value-problems-of-fractional-differential-equations-involving-stieltjes-derivatives" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/187408.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">40</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">816</span> Linear fractional differential equations for second kind modified Bessel functions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jorge%20Olivares">Jorge Olivares</a>, <a href="https://publications.waset.org/abstracts/search?q=Fernando%20Maass"> Fernando Maass</a>, <a href="https://publications.waset.org/abstracts/search?q=Pablo%20Martin"> Pablo Martin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Fractional derivatives have been considered recently as a way to solve different problems in Engineering. In this way, second kind modified Bessel functions are considered here. The order α fractional differential equations of second kind Bessel functions, Kᵥ(x), are studied with simple initial conditions. The Laplace transform and Caputo definition of fractional derivatives are considered. Solutions have been found for ν=1/3, 1/2, 2/3, -1/3, -1/2 and (-2/3). In these cases, the solutions are the sum of two hypergeometric functions. The α fractional derivatives have been for α=1/3, 1/2 and 2/3, and the above values of ν. No convergence has been found for the integer values of ν Furthermore when α has been considered as a rational found m/p, no general solution has been found. Clearly, this case is more difficult to treat than those of first kind Bessel Function. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Caputo" title="Caputo">Caputo</a>, <a href="https://publications.waset.org/abstracts/search?q=modified%20Bessel%20functions" title=" modified Bessel functions"> modified Bessel functions</a>, <a href="https://publications.waset.org/abstracts/search?q=hypergeometric" title=" hypergeometric"> hypergeometric</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20fractional%20differential%20equations" title=" linear fractional differential equations"> linear fractional differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=transform%20Laplace" title=" transform Laplace"> transform Laplace</a> </p> <a href="https://publications.waset.org/abstracts/91374/linear-fractional-differential-equations-for-second-kind-modified-bessel-functions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/91374.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">342</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">815</span> Hypergeometric Solutions to Linear Nonhomogeneous Fractional Equations with Spherical Bessel Functions of the First Kind</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Pablo%20Martin">Pablo Martin</a>, <a href="https://publications.waset.org/abstracts/search?q=Jorge%20Olivares"> Jorge Olivares</a>, <a href="https://publications.waset.org/abstracts/search?q=Fernando%20Maass"> Fernando Maass</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The use of fractional derivatives to different problems in Engineering and Physics has been increasing in the last decade. For this reason, we have here considered partial derivatives when the integral is a spherical Bessel function of the first kind in both regular and modified ones simple initial conditions have been also considered. In this way, the solution has been found as a combination of hypergeometric functions. The case of a general rational value for α of the fractional derivative α has been solved in a general way for alpha between zero and two. The modified spherical Bessel functions of the first kind have been also considered and how to go from the regular case to the modified one will be also shown. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=caputo%20fractional%20derivatives" title="caputo fractional derivatives">caputo fractional derivatives</a>, <a href="https://publications.waset.org/abstracts/search?q=hypergeometric%20functions" title=" hypergeometric functions"> hypergeometric functions</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20differential%20equations" title=" linear differential equations"> linear differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=spherical%20Bessel%20functions" title=" spherical Bessel functions"> spherical Bessel functions</a> </p> <a href="https://publications.waset.org/abstracts/91343/hypergeometric-solutions-to-linear-nonhomogeneous-fractional-equations-with-spherical-bessel-functions-of-the-first-kind" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/91343.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">325</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">814</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">813</span> Analytical Solutions of Time Space Fractional, Advection-Dispersion and Whitham-Broer-Kaup Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Muhammad%20Danish%20Khan">Muhammad Danish Khan</a>, <a href="https://publications.waset.org/abstracts/search?q=Imran%20Naeem"> Imran Naeem</a>, <a href="https://publications.waset.org/abstracts/search?q=Mudassar%20Imran"> Mudassar Imran</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this article, we study time-space Fractional Advection-Dispersion (FADE) equation and time-space Fractional Whitham-Broer-Kaup (FWBK) equation that have a significant role in hydrology. We introduce suitable transformations to convert fractional order derivatives to integer order derivatives and as a result these equations transform into Partial Differential Equations (PDEs). Then the Lie symmetries and corresponding optimal systems of the resulting PDEs are derived. The symmetry reductions and exact independent solutions based on optimal system are investigated which constitute the exact solutions of original fractional differential equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=modified%20Riemann-Liouville%20fractional%20derivative" title="modified Riemann-Liouville fractional derivative">modified Riemann-Liouville fractional derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=lie-symmetries" title=" lie-symmetries"> lie-symmetries</a>, <a href="https://publications.waset.org/abstracts/search?q=optimal%20system" title=" optimal system"> optimal system</a>, <a href="https://publications.waset.org/abstracts/search?q=invariant%20solutions" title=" invariant solutions"> invariant solutions</a> </p> <a href="https://publications.waset.org/abstracts/2191/analytical-solutions-of-time-space-fractional-advection-dispersion-and-whitham-broer-kaup-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/2191.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">431</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">812</span> Magnetohydrodynamic Couette Flow of Fractional Burger’s Fluid in an Annulus</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sani%20Isa">Sani Isa</a>, <a href="https://publications.waset.org/abstracts/search?q=Ali%20Musa"> Ali Musa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Burgers’ fluid with a fractional derivatives model in an annulus was analyzed. Combining appropriately the basic equations, with the fractionalized fractional Burger’s fluid model allow us to determine the velocity field, temperature and shear stress. The governing partial differential equation was solved using the combine Laplace transformation method and Riemann sum approximation to give velocity field, temperature and shear stress on the fluid flow. The influence of various parameters like fractional parameters, relaxation time and retardation time, are drawn. The results obtained are simulated using Mathcad software and presented graphically. From the graphical results, we observed that the relaxation time and time helps the flow pattern, on the other hand, other material constants resist the fluid flow while fractional parameters effect on fluid flow is opposite to each other. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=sani%20isa" title="sani isa">sani isa</a>, <a href="https://publications.waset.org/abstracts/search?q=Ali%20musaburger%E2%80%99s%20fluid" title=" Ali musaburger’s fluid"> Ali musaburger’s fluid</a>, <a href="https://publications.waset.org/abstracts/search?q=Laplace%20transform" title=" Laplace transform"> Laplace transform</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20derivatives" title=" fractional derivatives"> fractional derivatives</a>, <a href="https://publications.waset.org/abstracts/search?q=annulus" title=" annulus"> annulus</a> </p> <a href="https://publications.waset.org/abstracts/190150/magnetohydrodynamic-couette-flow-of-fractional-burgers-fluid-in-an-annulus" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/190150.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">24</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">811</span> On the Solution of Fractional-Order Dynamical Systems Endowed with Block Hybrid Methods</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kizito%20Ugochukwu%20Nwajeri">Kizito Ugochukwu Nwajeri</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents a distinct approach to solving fractional dynamical systems using hybrid block methods (HBMs). Fractional calculus extends the concept of derivatives and integrals to non-integer orders and finds increasing application in fields such as physics, engineering, and finance. However, traditional numerical techniques often struggle to accurately capture the complex behaviors exhibited by these systems. To address this challenge, we develop HBMs that integrate single-step and multi-step methods, enabling the simultaneous computation of multiple solution points while maintaining high accuracy. Our approach employs polynomial interpolation and collocation techniques to derive a system of equations that effectively models the dynamics of fractional systems. We also directly incorporate boundary and initial conditions into the formulation, enhancing the stability and convergence properties of the numerical solution. An adaptive step-size mechanism is introduced to optimize performance based on the local behavior of the solution. Extensive numerical simulations are conducted to evaluate the proposed methods, demonstrating significant improvements in accuracy and efficiency compared to traditional numerical approaches. The results indicate that our hybrid block methods are robust and versatile, making them suitable for a wide range of applications involving fractional dynamical systems. This work contributes to the existing literature by providing an effective numerical framework for analyzing complex behaviors in fractional systems, thereby opening new avenues for research and practical implementation across various disciplines. <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=numerical%20simulation" title=" numerical simulation"> numerical simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=stability%20and%20convergence" title=" stability and convergence"> stability and convergence</a>, <a href="https://publications.waset.org/abstracts/search?q=Adaptive%20step-size%20mechanism" title=" Adaptive step-size mechanism"> Adaptive step-size mechanism</a>, <a href="https://publications.waset.org/abstracts/search?q=collocation%20methods" title=" collocation methods"> collocation methods</a> </p> <a href="https://publications.waset.org/abstracts/188911/on-the-solution-of-fractional-order-dynamical-systems-endowed-with-block-hybrid-methods" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/188911.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">43</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">810</span> Numerical Solution of Magneto-Hydrodynamic Flow of a Viscous Fluid in the Presence of Nanoparticles with Fractional Derivatives through a Cylindrical Tube</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Muhammad%20Abdullah">Muhammad Abdullah</a>, <a href="https://publications.waset.org/abstracts/search?q=Asma%20Rashid%20Butt"> Asma Rashid Butt</a>, <a href="https://publications.waset.org/abstracts/search?q=Nauman%20Raza"> Nauman Raza</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Biomagnetic fluids like blood play key role in different applications of medical science and bioengineering. In this paper, the magnetohydrodynamic flow of a viscous fluid with magnetic particles through a cylindrical tube is investigated. The fluid is electrically charged in the presence of a uniform external magnetic field. The movement in the fluid is produced due to the cylindrical tube. Initially, the fluid and tube are at rest and at time t=0⁺, the tube starts to move along its axis. To obtain the mathematical model of flow with fractional derivatives fractional calculus approach is used. The solution of the flow model is obtained by using Laplace transformation. The Simon's numerical algorithm is employed to obtain inverse Laplace transform. The hybrid technique, we are employing has less computational effort as compared to other methods. The numerical calculations have been performed with Mathcad software. As the special cases of our problem, the solution of flow model with ordinary derivatives and flow without magnetic particles has been procured. Finally, the impact of non-integer fractional parameter alpha, Hartmann number Ha, and Reynolds number Re on flow and magnetic particles velocity is analyzed and depicted by graphs. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=viscous%20fluid" title="viscous fluid">viscous fluid</a>, <a href="https://publications.waset.org/abstracts/search?q=magnetic%20particles" title=" magnetic particles"> magnetic particles</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=laplace%20transformation" title=" laplace transformation"> laplace transformation</a> </p> <a href="https://publications.waset.org/abstracts/90032/numerical-solution-of-magneto-hydrodynamic-flow-of-a-viscous-fluid-in-the-presence-of-nanoparticles-with-fractional-derivatives-through-a-cylindrical-tube" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/90032.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">206</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">809</span> Nonhomogeneous Linear Fractional Differential Equations Will Bessel Functions of the First Kind Giving Hypergeometric Functions Solutions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fernando%20Maass">Fernando Maass</a>, <a href="https://publications.waset.org/abstracts/search?q=Pablo%20Martin"> Pablo Martin</a>, <a href="https://publications.waset.org/abstracts/search?q=Jorge%20Olivares"> Jorge Olivares</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Fractional derivatives have become very important in several areas of Engineering, however, the solutions of simple differential equations are not known. Here we are considering the simplest first order nonhomogeneous differential equations with Bessel regular functions of the first kind, in this way the solutions have been found which are hypergeometric solutions for any fractional derivative of order α, where α is rational number α=m/p, between zero and one. The way to find this result is by using Laplace transform and the Caputo definitions of fractional derivatives. This method is for values longer than one. However for α entire number the hypergeometric functions are Kumer type, no integer values of alpha, the hypergeometric function is more complicated is type ₂F₃(a,b,c, t2/2). The argument of the hypergeometric changes sign when we go from the regular Bessel functions to the modified Bessel functions of the first kind, however it integer seems that using precise values of α and considering no integers values of α, a solution can be obtained in terms of two hypergeometric functions. Further research is required for future papers in order to obtain the general solution for any rational value of α. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Caputo" title="Caputo">Caputo</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20calculation" title=" fractional calculation"> fractional calculation</a>, <a href="https://publications.waset.org/abstracts/search?q=hypergeometric" title=" hypergeometric"> hypergeometric</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20differential%20equations" title=" linear differential equations"> linear differential equations</a> </p> <a href="https://publications.waset.org/abstracts/91373/nonhomogeneous-linear-fractional-differential-equations-will-bessel-functions-of-the-first-kind-giving-hypergeometric-functions-solutions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/91373.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">197</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">808</span> A Study on Stochastic Integral Associated with Catastrophes</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Reni%20Sagayaraj">M. Reni Sagayaraj</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Anand%20Gnana%20Selvam"> S. Anand Gnana Selvam</a>, <a href="https://publications.waset.org/abstracts/search?q=R.%20Reynald%20Susainathan"> R. Reynald Susainathan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We analyze stochastic integrals associated with a mutation process. To be specific, we describe the cell population process and derive the differential equations for the joint generating functions for the number of mutants and their integrals in generating functions and their applications. We obtain first-order moments of the processes of the two-way mutation process in first-order moment structure of X (t) and Y (t) and the second-order moments of a one-way mutation process. In this paper, we obtain the limiting behaviour of the integrals in limiting distributions of X (t) and Y (t). <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=stochastic%20integrals" title="stochastic integrals">stochastic integrals</a>, <a href="https://publications.waset.org/abstracts/search?q=single%E2%80%93server%20queue%20model" title=" single–server queue model"> single–server queue model</a>, <a href="https://publications.waset.org/abstracts/search?q=catastrophes" title=" catastrophes"> catastrophes</a>, <a href="https://publications.waset.org/abstracts/search?q=busy%20period" title=" busy period"> busy period</a> </p> <a href="https://publications.waset.org/abstracts/21325/a-study-on-stochastic-integral-associated-with-catastrophes" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/21325.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">642</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">807</span> Effects of the Fractional Order on Nanoparticles in Blood Flow through the Stenosed Artery</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohammed%20Abdulhameed">Mohammed Abdulhameed</a>, <a href="https://publications.waset.org/abstracts/search?q=Sagir%20M.%20Abdullahi"> Sagir M. Abdullahi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, based on the applications of nanoparticle, the blood flow along with nanoparticles through stenosed artery is studied. The blood is acted by periodic body acceleration, an oscillating pressure gradient and an external magnetic field. The mathematical formulation is based on Caputo-Fabrizio fractional derivative without singular kernel. The model of ordinary blood, corresponding to time-derivatives of integer order, is obtained as a limiting case. Analytical solutions of the blood velocity and temperature distribution are obtained by means of the Hankel and Laplace transforms. Effects of the order of Caputo-Fabrizio time-fractional derivatives and three different nanoparticles i.e. Fe3O4, TiO4 and Cu are studied. The results highlights that, models with fractional derivatives bring significant differences compared to the ordinary model. It is observed that the addition of Fe3O4 nanoparticle reduced the resistance impedance of the blood flow and temperature distribution through bell shape stenosed arteries as compared to TiO4 and Cu nanoparticles. On entering in the stenosed area, blood temperature increases slightly, but, increases considerably and reaches its maximum value in the stenosis throat. The shears stress has variation from a constant in the area without stenosis and higher in the layers located far to the longitudinal axis of the artery. This fact can be an important for some clinical applications in therapeutic procedures. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nanoparticles" title="nanoparticles">nanoparticles</a>, <a href="https://publications.waset.org/abstracts/search?q=blood%20flow" title=" blood flow"> blood flow</a>, <a href="https://publications.waset.org/abstracts/search?q=stenosed%20%20artery" title=" stenosed artery"> stenosed artery</a>, <a href="https://publications.waset.org/abstracts/search?q=mathematical%20models" title=" mathematical models"> mathematical models</a> </p> <a href="https://publications.waset.org/abstracts/58237/effects-of-the-fractional-order-on-nanoparticles-in-blood-flow-through-the-stenosed-artery" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/58237.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">267</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">806</span> Dynamical Analysis of the Fractional-Order Mathematical Model of Hashimoto’s Thyroiditis</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Neelam%20Singha">Neelam Singha</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The present work intends to analyze the system dynamics of Hashimoto’s thyroiditis with the assistance of fractional calculus. Hashimoto’s thyroiditis or chronic lymphocytic thyroiditis is an autoimmune disorder in which the immune system attacks the thyroid gland, which gradually results in interrupting the normal thyroid operation. Consequently, the feedback control of the system gets disrupted due to thyroid follicle cell lysis. And, the patient perceives life-threatening clinical conditions like goiter, hyperactivity, euthyroidism, hyperthyroidism, etc. In this work, we aim to obtain the approximate solution to the posed fractional-order problem describing Hashimoto’s thyroiditis. We employ the Adomian decomposition method to solve the system of fractional-order differential equations, and the solutions obtained shall be useful to provide information about the effect of medical care. The numerical technique is executed in an organized manner to furnish the associated details of the progression of the disease and to visualize it graphically with suitable plots. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=adomian%20decomposition%20method" title="adomian decomposition method">adomian decomposition method</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20derivatives" title=" fractional derivatives"> fractional derivatives</a>, <a href="https://publications.waset.org/abstracts/search?q=Hashimoto%27s%20thyroiditis" title=" Hashimoto's thyroiditis"> Hashimoto's thyroiditis</a>, <a href="https://publications.waset.org/abstracts/search?q=mathematical%20modeling" title=" mathematical modeling"> mathematical modeling</a> </p> <a href="https://publications.waset.org/abstracts/139240/dynamical-analysis-of-the-fractional-order-mathematical-model-of-hashimotos-thyroiditis" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/139240.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">211</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">805</span> Approximations of Fractional Derivatives and Its Applications in Solving Non-Linear Fractional Variational Problems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Harendra%20Singh">Harendra Singh</a>, <a href="https://publications.waset.org/abstracts/search?q=Rajesh%20Pandey"> Rajesh Pandey</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper presents a numerical method based on operational matrix of integration and Ryleigh method for the solution of a class of non-linear fractional variational problems (NLFVPs). Chebyshev first kind polynomials are used for the construction of operational matrix. Using operational matrix and Ryleigh method the NLFVP is converted into a system of non-linear algebraic equations, and solving these equations we obtained approximate solution for NLFVPs. Convergence analysis of the proposed method is provided. Numerical experiment is done to show the applicability of the proposed numerical method. The obtained numerical results are compared with exact solution and solution obtained from Chebyshev third kind. Further the results are shown graphically for different fractional order involved in the problems. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=non-linear%20fractional%20variational%20problems" title="non-linear fractional variational problems">non-linear fractional variational problems</a>, <a href="https://publications.waset.org/abstracts/search?q=Rayleigh-Ritz%20method" title=" Rayleigh-Ritz method"> Rayleigh-Ritz method</a>, <a href="https://publications.waset.org/abstracts/search?q=convergence%20analysis" title=" convergence analysis"> convergence analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=error%20analysis" title=" error analysis"> error analysis</a> </p> <a href="https://publications.waset.org/abstracts/57497/approximations-of-fractional-derivatives-and-its-applications-in-solving-non-linear-fractional-variational-problems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/57497.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">298</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">804</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">803</span> Chebyshev Wavelets and Applications</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Emanuel%20Guariglia">Emanuel Guariglia</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper we deal with Chebyshev wavelets. We analyze their properties computing their Fourier transform. Moreover, we discuss the differential properties of Chebyshev wavelets due the connection coefficients. The differential properties of Chebyshev wavelets, expressed by the connection coefficients (also called refinable integrals), are given by finite series in terms of the Kronecker delta. Moreover, we treat the p-order derivative of Chebyshev wavelets and compute its Fourier transform. Finally, we expand the mother wavelet in Taylor series with an application both in fractional calculus and fractal geometry. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chebyshev%20wavelets" title="Chebyshev wavelets">Chebyshev wavelets</a>, <a href="https://publications.waset.org/abstracts/search?q=Fourier%20transform" title=" Fourier transform"> Fourier transform</a>, <a href="https://publications.waset.org/abstracts/search?q=connection%20coefficients" title=" connection coefficients"> connection coefficients</a>, <a href="https://publications.waset.org/abstracts/search?q=Taylor%20series" title=" Taylor series"> Taylor series</a>, <a href="https://publications.waset.org/abstracts/search?q=local%20fractional%20derivative" title=" local fractional derivative"> local fractional derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=Cantor%20set" title=" Cantor set"> Cantor set</a> </p> <a href="https://publications.waset.org/abstracts/157194/chebyshev-wavelets-and-applications" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/157194.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">123</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">802</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">801</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">800</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">799</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">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">798</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">797</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">796</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">795</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">794</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" 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