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fractional derivative</title> <meta name="description" content="Search results for: local fractional derivative"> <meta name="keywords" content="local fractional derivative"> <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 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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="local fractional derivative"> <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> 5939</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: local fractional derivative</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5939</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">5938</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">5937</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">5936</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">5935</span> A Dynamical Study of Fractional Order Obesity Model by a Combined Legendre Wavelet Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hakiki%20Kheira">Hakiki Kheira</a>, <a href="https://publications.waset.org/abstracts/search?q=Belhamiti%20Omar"> Belhamiti Omar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we propose a new compartmental fractional order model for the simulation of epidemic obesity dynamics. Using the Legendre wavelet method combined with the decoupling and quasi-linearization technique, we demonstrate the validity and applicability of our model. We also present some fractional differential illustrative examples to demonstrate the applicability and efficiency of the method. The fractional derivative is described in the Caputo sense. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Caputo%20derivative" title="Caputo derivative">Caputo derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=epidemiology" title=" epidemiology"> epidemiology</a>, <a href="https://publications.waset.org/abstracts/search?q=Legendre%20wavelet%20method" title=" Legendre wavelet method"> Legendre wavelet method</a>, <a href="https://publications.waset.org/abstracts/search?q=obesity" title=" obesity "> obesity </a> </p> <a href="https://publications.waset.org/abstracts/42731/a-dynamical-study-of-fractional-order-obesity-model-by-a-combined-legendre-wavelet-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/42731.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">421</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">5934</span> A Fractional Derivative Model to Quantify Non-Darcy Flow in Porous and Fractured Media</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Golden%20J.%20Zhang">Golden J. Zhang</a>, <a href="https://publications.waset.org/abstracts/search?q=Dongbao%20Zhou"> Dongbao Zhou</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Darcy’s law is the fundamental theory in fluid dynamics and engineering applications. Although Darcy linearity was found to be valid for slow, viscous flow, non-linear and non-Darcian flow has been well documented under both small and large velocity fluid flow. Various classical models were proposed and used widely to quantify non-Darcian flow, including the well-known Forchheimer, Izbash, and Swartzendruber models. Applications, however, revealed limitations of these models. Here we propose a general model built upon the Caputo fractional derivative to quantify non-Darcian flow for various flows (laminar to turbulence).Real-world applications and model comparisons showed that the new fractional-derivative model, which extends the fractional model proposed recently by Zhou and Yang (2018), can capture the non-Darcian flow in the relatively small velocity in low-permeability deposits and the relatively high velocity in high-permeability sand. A scale effect was also identified for non-Darcian flow in fractured rocks. Therefore, fractional calculus may provide an efficient tool to improve classical models to quantify fluid dynamics in aquatic environments. <p class="card-text"><strong>Keywords:</strong> <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=darcy%E2%80%99s%20law" title=" darcy’s law"> darcy’s law</a>, <a href="https://publications.waset.org/abstracts/search?q=non-darcian%20flow" title=" non-darcian flow"> non-darcian flow</a>, <a href="https://publications.waset.org/abstracts/search?q=fluid%20dynamics" title=" fluid dynamics"> fluid dynamics</a> </p> <a href="https://publications.waset.org/abstracts/154329/a-fractional-derivative-model-to-quantify-non-darcy-flow-in-porous-and-fractured-media" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/154329.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">126</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">5933</span> Tuning Fractional Order Proportional-Integral-Derivative Controller Using Hybrid Genetic Algorithm Particle Swarm and Differential Evolution Optimization Methods for Automatic Voltage Regulator System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fouzi%20Aboura">Fouzi Aboura</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The fractional order proportional-integral-derivative (FOPID) controller or fractional order (PIλDµ) is a proportional-integral-derivative (PID) controller where integral order (λ) and derivative order (µ) are fractional, one of the important application of classical PID is the Automatic Voltage Regulator (AVR).The FOPID controller needs five parameters optimization while the design of conventional PID controller needs only three parameters to be optimized. In our paper we have proposed a comparison between algorithms Differential Evolution (DE) and Hybrid Genetic Algorithm Particle Swarm Optimization (HGAPSO) ,we have studied theirs characteristics and performance analysis to find an optimum parameters of the FOPID controller, a new objective function is also proposed to take into account the relation between the performance criteria’s. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=FOPID%20controller" title="FOPID controller">FOPID controller</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20order" title=" fractional order"> fractional order</a>, <a href="https://publications.waset.org/abstracts/search?q=AVR%20system" title=" AVR system"> AVR system</a>, <a href="https://publications.waset.org/abstracts/search?q=objective%20function" title=" objective function"> objective function</a>, <a href="https://publications.waset.org/abstracts/search?q=optimization" title=" optimization"> optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=GA" title=" GA"> GA</a>, <a href="https://publications.waset.org/abstracts/search?q=PSO" title=" PSO"> PSO</a>, <a href="https://publications.waset.org/abstracts/search?q=HGAPSO" title=" HGAPSO"> HGAPSO</a> </p> <a href="https://publications.waset.org/abstracts/164900/tuning-fractional-order-proportional-integral-derivative-controller-using-hybrid-genetic-algorithm-particle-swarm-and-differential-evolution-optimization-methods-for-automatic-voltage-regulator-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/164900.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">90</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">5932</span> Numerical Solutions of Fractional Order Epidemic Model</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>, <a href="https://publications.waset.org/abstracts/search?q=Ayesha%20Sohail"> Ayesha Sohail</a>, <a href="https://publications.waset.org/abstracts/search?q=Sana%20Javed"> Sana Javed</a>, <a href="https://publications.waset.org/abstracts/search?q=Khadija%20Maqbool"> Khadija Maqbool</a>, <a href="https://publications.waset.org/abstracts/search?q=Salma%20Kanwal"> Salma Kanwal</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The dynamical study of the carriers play an essential role in the evolution and global transmission of infectious diseases and will be discussed in this study. To make this approach novel, we will consider the fractional order model which is generalization of integer order derivative to an arbitrary number. Since the integration involved is non local therefore this property of fractional operator is very useful to study epidemic model for infectious diseases. An extended numerical method (ODE solver) is implemented on the model equations and we will present the simulations of the model for diﬀerent values of fractional order to study the eﬀect of carriers on transmission dynamics. Global dynamics of fractional model are established by using the reproduction number. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fractional%20di%EF%AC%80erential%20equation" title="Fractional diﬀerential equation">Fractional diﬀerential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Numerical%20simulations" title=" Numerical simulations"> Numerical simulations</a>, <a href="https://publications.waset.org/abstracts/search?q=epidemic%20model" title=" epidemic model"> epidemic model</a>, <a href="https://publications.waset.org/abstracts/search?q=transmission%20dynamics" title=" transmission dynamics"> transmission dynamics</a> </p> <a href="https://publications.waset.org/abstracts/17447/numerical-solutions-of-fractional-order-epidemic-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17447.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">602</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">5931</span> Nonlocal Phenomena in Quantum Mechanics</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kazim%20G.%20Atman">Kazim G. Atman</a>, <a href="https://publications.waset.org/abstracts/search?q=H%C3%BCseyin%20Sirin"> Hüseyin Sirin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In theoretical physics, nonlocal phenomena has always been subject of debate. However, in the conventional mathematical approach where the developments of the physical systems are investigated by using the standard mathematical tools, nonlocal effects are not taken into account. In order to investigate the nonlocality in quantum mechanics and fractal property of space, fractional derivative operators are employed in this study. In this manner, fractional creation and annihilation operators are introduced and Einstein coefficients are taken into account as an application of concomitant formalism in quantum field theory. Therefore, each energy mode of photons are considered as fractional quantized harmonic oscillator hereby Einstein coefficients are obtained. Nevertheless, wave function and energy eigenvalues of fractional quantum mechanical harmonic oscillator are obtained via the fractional derivative order α which is a measure of the influence of nonlocal effects. In the case α = 1, where space becomes homogeneous and continuous, standard physical conclusions are recovered. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Einstein%E2%80%99s%20Coefficients" title="Einstein’s Coefficients">Einstein’s Coefficients</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%20Quantum%20Mechanics" title=" Fractional Quantum Mechanics"> Fractional Quantum Mechanics</a>, <a href="https://publications.waset.org/abstracts/search?q=Nonlocal%20Theories" title=" Nonlocal Theories"> Nonlocal Theories</a> </p> <a href="https://publications.waset.org/abstracts/124566/nonlocal-phenomena-in-quantum-mechanics" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/124566.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">170</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">5930</span> Modeling the Compound Interest Dynamics Using Fractional Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Muath%20Awadalla">Muath Awadalla</a>, <a href="https://publications.waset.org/abstracts/search?q=Maen%20Awadallah"> Maen Awadallah</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Banking sector covers different activities including lending money to customers. However, it is commonly known that customers pay money they have borrowed including an added amount called interest. Compound interest rate is an approach used in determining the interest to be paid. The instant compounded amount to be paid by a debtor is obtained through a differential equation whose main parameters are the rate and the time. The rate used by banks in a country is often defined by the government of the said country. In Switzerland, for instance, a negative rate was once applied. In this work, a new approach of modeling the compound interest is proposed using Hadamard fractional derivative. As a result, it appears that depending on the fraction value used in derivative the amount to be paid by a debtor might either be higher or lesser than the amount determined using the classical approach. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=compound%20interest" title="compound interest">compound interest</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20differential%20equation" title=" fractional differential equation"> fractional differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=hadamard%20fractional%20derivative" title=" hadamard fractional derivative"> hadamard fractional derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=optimization" title=" optimization"> optimization</a> </p> <a href="https://publications.waset.org/abstracts/110859/modeling-the-compound-interest-dynamics-using-fractional-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/110859.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">126</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">5929</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">5928</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">5927</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">5926</span> Multiple Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Guezane-Lakoud">A. Guezane-Lakoud</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Bensebaa"> S. Bensebaa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we study a boundary value problem of nonlinear fractional differential equation. Existence and positivity results of solutions are obtained. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=positive%20solution" title="positive solution">positive solution</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20caputo%20derivative" title=" fractional caputo derivative"> fractional caputo derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=Banach%20contraction%20principle" title=" Banach contraction principle"> Banach contraction principle</a>, <a href="https://publications.waset.org/abstracts/search?q=Avery%20and%20Peterson%20fixed%20point%20theorem" title=" Avery and Peterson fixed point theorem"> Avery and Peterson fixed point theorem</a> </p> <a href="https://publications.waset.org/abstracts/17545/multiple-positive-solutions-for-boundary-value-problem-of-nonlinear-fractional-differential-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17545.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">414</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">5925</span> Application of a SubIval Numerical Solver for Fractional Circuits</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Marcin%20Sowa">Marcin Sowa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper discusses the subinterval-based numerical method for fractional derivative computations. It is now referred to by its acronym – SubIval. The basis of the method is briefly recalled. The ability of the method to be applied in time stepping solvers is discussed. The possibility of implementing a time step size adaptive solver is also mentioned. The solver is tested on a transient circuit example. In order to display the accuracy of the solver – the results have been compared with those obtained by means of a semi-analytical method called gcdAlpha. The time step size adaptive solver applying SubIval has been proven to be very accurate as the results are very close to the referential solution. The solver is currently able to solve FDE (fractional differential equations) with various derivative orders for each equation and any type of source time functions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=numerical%20method" title="numerical method">numerical method</a>, <a href="https://publications.waset.org/abstracts/search?q=SubIval" title=" SubIval"> SubIval</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=numerical%20solver" title=" numerical solver"> numerical solver</a>, <a href="https://publications.waset.org/abstracts/search?q=circuit%20analysis" title=" circuit analysis"> circuit analysis</a> </p> <a href="https://publications.waset.org/abstracts/97566/application-of-a-subival-numerical-solver-for-fractional-circuits" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/97566.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">5924</span> Optimization of Coefficients of Fractional Order Proportional-Integrator-Derivative Controller on Permanent Magnet Synchronous Motors Using Particle Swarm Optimization</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ali%20Motalebi%20Saraji">Ali Motalebi Saraji</a>, <a href="https://publications.waset.org/abstracts/search?q=Reza%20Zarei%20Lamuki"> Reza Zarei Lamuki</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Speed control and behavior improvement of permanent magnet synchronous motors (PMSM) that have reliable performance, low loss, and high power density, especially in industrial drives, are of great importance for researchers. Because of its importance in this paper, coefficients optimization of proportional-integrator-derivative fractional order controller is presented using Particle Swarm Optimization (PSO) algorithm in order to improve the behavior of PMSM in its speed control loop. This improvement is simulated in MATLAB software for the proposed optimized proportional-integrator-derivative fractional order controller with a Genetic algorithm and compared with a full order controller with a classic optimization method. Simulation results show the performance improvement of the proposed controller with respect to two other controllers in terms of rising time, overshoot, and settling time. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=speed%20control%20loop%20of%20permanent%20magnet%20synchronous%20motor" title="speed control loop of permanent magnet synchronous motor">speed control loop of permanent magnet synchronous motor</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20and%20full%20order%20proportional-integrator-derivative%20controller" title=" fractional and full order proportional-integrator-derivative controller"> fractional and full order proportional-integrator-derivative controller</a>, <a href="https://publications.waset.org/abstracts/search?q=coefficients%20optimization" title=" coefficients optimization"> coefficients optimization</a>, <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=improvement%20of%20behavior" title=" improvement of behavior"> improvement of behavior</a> </p> <a href="https://publications.waset.org/abstracts/129038/optimization-of-coefficients-of-fractional-order-proportional-integrator-derivative-controller-on-permanent-magnet-synchronous-motors-using-particle-swarm-optimization" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/129038.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">146</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">5923</span> Operational Matrix Method for Fuzzy Fractional Reaction Diffusion Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sachin%20Kumar">Sachin Kumar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20PDE" title="fractional PDE">fractional PDE</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20valued%20function" title=" fuzzy valued function"> fuzzy valued function</a>, <a href="https://publications.waset.org/abstracts/search?q=diffusion%20equation" title=" diffusion equation"> diffusion equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Legendre%20polynomial" title=" Legendre polynomial"> Legendre polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=spectral%20method" title=" spectral method"> spectral method</a> </p> <a href="https://publications.waset.org/abstracts/125273/operational-matrix-method-for-fuzzy-fractional-reaction-diffusion-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/125273.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">201</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">5922</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">5921</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">5920</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">5919</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">5918</span> Analytical Soliton Solutions of the Fractional Jaulent-Miodek System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sajeda%20Elbashabsheh">Sajeda Elbashabsheh</a>, <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> This paper applies a modified Laplace Adomian decomposition method to solve the time-fractional JaulentMiodek system. The method produce convergent series solutions with easily compatible components. This paper considers the Caputo fractional derivative. The effectiveness and applicability of the method are demonstrated by comparing its results with those of prior studies. Results are presented in tables and figures. These solutions might be imperative and significant for the explanation of some practical physical phenomena. All computations and figures in the work are done using MATHEMATICA. The numerical results demonstrate that the current methods are effective, reliable, and simple to i implement for nonlinear fractional partial differential equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=approximate%20solutions" title="approximate solutions">approximate solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=Jaulent-Miodek%20system" title=" Jaulent-Miodek system"> Jaulent-Miodek system</a>, <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=solitons" title=" solitons"> solitons</a> </p> <a href="https://publications.waset.org/abstracts/186620/analytical-soliton-solutions-of-the-fractional-jaulent-miodek-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/186620.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">44</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">5917</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">5916</span> Cellular Automata Using Fractional Integral Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yasser%20F.%20Hassan">Yasser F. Hassan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a proposed model of cellular automata is studied by means of fractional integral function. A cellular automaton is a decentralized computing model providing an excellent platform for performing complex computation with the help of only local information. The paper discusses how using fractional integral function for representing cellular automata memory or state. The architecture of computing and learning model will be given and the results of calibrating of approach are also given. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20integral" title="fractional integral">fractional integral</a>, <a href="https://publications.waset.org/abstracts/search?q=cellular%20automata" title=" cellular automata"> cellular automata</a>, <a href="https://publications.waset.org/abstracts/search?q=memory" title=" memory"> memory</a>, <a href="https://publications.waset.org/abstracts/search?q=learning" title=" learning"> learning</a> </p> <a href="https://publications.waset.org/abstracts/55312/cellular-automata-using-fractional-integral-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/55312.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">413</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">5915</span> A New Fuzzy Fractional Order Model of Transmission of Covid-19 With Quarantine Class</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Asma%20Hanif">Asma Hanif</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20I.%20K.%20Butt"> A. I. K. Butt</a>, <a href="https://publications.waset.org/abstracts/search?q=Shabir%20Ahmad"> Shabir Ahmad</a>, <a href="https://publications.waset.org/abstracts/search?q=Rahim%20Ud%20Din"> Rahim Ud Din</a>, <a href="https://publications.waset.org/abstracts/search?q=Mustafa%20Inc"> Mustafa Inc</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper is devoted to a study of the fuzzy fractional mathematical model reviewing the transmission dynamics of the infectious disease Covid-19. The proposed dynamical model consists of susceptible, exposed, symptomatic, asymptomatic, quarantine, hospitalized and recovered compartments. In this study, we deal with the fuzzy fractional model defined in Caputo’s sense. We show the positivity of state variables that all the state variables that represent different compartments of the model are positive. Using Gronwall inequality, we show that the solution of the model is bounded. Using the notion of the next-generation matrix, we find the basic reproduction number of the model. We demonstrate the local and global stability of the equilibrium point by using the concept of Castillo-Chavez and Lyapunov theory with the Lasalle invariant principle, respectively. We present the results that reveal the existence and uniqueness of the solution of the considered model through the fixed point theorem of Schauder and Banach. Using the fuzzy hybrid Laplace method, we acquire the approximate solution of the proposed model. The results are graphically presented via MATLAB-17. <p class="card-text"><strong>Keywords:</strong> <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=existence%20and%20uniqueness" title=" existence and uniqueness"> existence and uniqueness</a>, <a href="https://publications.waset.org/abstracts/search?q=gronwall%20inequality" title=" gronwall inequality"> gronwall inequality</a>, <a href="https://publications.waset.org/abstracts/search?q=Lyapunov%20theory" title=" Lyapunov theory"> Lyapunov theory</a> </p> <a href="https://publications.waset.org/abstracts/147667/a-new-fuzzy-fractional-order-model-of-transmission-of-covid-19-with-quarantine-class" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/147667.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">105</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">5914</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">5913</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">5912</span> Numerical Solution of Space Fractional Order Linear/Nonlinear Reaction-Advection Diffusion Equation Using Jacobi Polynomial</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shubham%20Jaiswal">Shubham Jaiswal</a> </p> <p class="card-text"><strong>Abstract:</strong></p> During modelling of many physical problems and engineering processes, fractional calculus plays an important role. Those are greatly described by fractional differential equations (FDEs). So a reliable and efficient technique to solve such types of FDEs is needed. In this article, a numerical solution of a class of fractional differential equations namely space fractional order reaction-advection dispersion equations subject to initial and boundary conditions is derived. In the proposed approach shifted Jacobi polynomials are used to approximate the solutions together with shifted Jacobi operational matrix of fractional order and spectral collocation method. The main advantage of this approach is that it converts such problems in the systems of algebraic equations which are easier to be solved. The proposed approach is effective to solve the linear as well as non-linear FDEs. To show the reliability, validity and high accuracy of proposed approach, the numerical results of some illustrative examples are reported, which are compared with the existing analytical results already reported in the literature. The error analysis for each case exhibited through graphs and tables confirms the exponential convergence rate of the proposed method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=space%20fractional%20order%20linear%2Fnonlinear%20reaction-advection%20diffusion%20equation" title="space fractional order linear/nonlinear reaction-advection diffusion equation">space fractional order linear/nonlinear reaction-advection diffusion equation</a>, <a href="https://publications.waset.org/abstracts/search?q=shifted%20Jacobi%20polynomials" title=" shifted Jacobi polynomials"> shifted Jacobi polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=operational%20matrix" title=" operational matrix"> operational matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=collocation%20method" title=" collocation method"> collocation method</a>, <a href="https://publications.waset.org/abstracts/search?q=Caputo%20derivative" title=" Caputo derivative"> Caputo derivative</a> </p> <a href="https://publications.waset.org/abstracts/79521/numerical-solution-of-space-fractional-order-linearnonlinear-reaction-advection-diffusion-equation-using-jacobi-polynomial" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/79521.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">445</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">5911</span> A Coupled System of Caputo-Type Katugampola Fractional Differential Equations with Integral Boundary Conditions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yacine%20Arioua">Yacine Arioua</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we investigate the existence and uniqueness of solutions for a coupled system of nonlinear Caputo-type Katugampola fractional differential equations with integral boundary conditions. Based upon a contraction mapping principle, Schauders fixed point theorems, some new existence and uniqueness results of solutions for the given problems are obtained. For application, some examples are given to illustrate the usefulness of our main results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20differential%20equations" title="fractional differential equations">fractional differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=coupled%20system" title=" coupled system"> coupled system</a>, <a href="https://publications.waset.org/abstracts/search?q=Caputo-Katugampola%20derivative" title=" Caputo-Katugampola derivative"> Caputo-Katugampola derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=fixed%20point%20theorems" title=" fixed point theorems"> fixed point theorems</a>, <a href="https://publications.waset.org/abstracts/search?q=existence" title=" existence"> existence</a>, <a href="https://publications.waset.org/abstracts/search?q=uniqueness" title=" uniqueness"> uniqueness</a> </p> <a href="https://publications.waset.org/abstracts/124953/a-coupled-system-of-caputo-type-katugampola-fractional-differential-equations-with-integral-boundary-conditions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/124953.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">264</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">5910</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 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