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11 articles for “Fractional Differential Equation”
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Research ArticleOpen accessPhrase in the titleAn Expansion Iterative Technique for Handling Fractional Differential Equations Using Fractional Power Series SchemeRadwan Abu-Gdairi, Mohammed Al-Smadi, Ghaleb GumahIn this study, we present a new analytical numerical technique for solving a class of time Fractional Differential Equations (FDEs) with variable coefficients based on the generalized Taylor series formula in the Caputo sense. This method provided the solution in the form of a rapidly convergent power series under a multiple fractional differentiability with easily computable components. An efficacious experiment … …Journal of Mathematics and Statistics, Vol. 11, Issue 2 · 18 Sep 2015 · 7,815 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleAnalytical Solutions of Riccati Fractional Equation with Coefficients Satisfying Differential Conditions with Arbitrary FunctionKhaled K. JaberNew exact solutions of the Fractional Riccati Differential equation are presented. Exact solutions are obtained in cases that the coefficient functions and an arbitrary function satisfy some differential conditions. In view of the conditions imposed on Riccati equation's coefficients we define and formulate the coefficients of the Riccati equation to obtain the differential cases, for each case the general solution … …Journal of Mathematics and Statistics, Vol. 13, Issue 4 · 27 Dec 2017 · 7,214 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleStudy of Fractional Order Integro-Differential Equations by using Chebyshev Neural NetworkSarkhosh S. Chaharborj, Shahriar S. Chaharborj, Yaghoub MahmoudiRecently fractional integro-differential equations have been proposed for the modeling of many complex systems. Simulation of these equations requires the development of suitable numerical methods. This paper is devoted to finding the numerical solution of some classes of fractional integro-differential equations by employing the Chebyshev Neural Network (ChNN). The accuracy of proposed method is shown by comparing the numerical results … …Journal of Mathematics and Statistics, Vol. 13, Issue 1 · 11 Feb 2017 · 7,406 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleApproximate Series Solution of Nonlinear, Fractional Klein-Gordon Equations Using Fractional Reduced Differential Transform MethodEman Abuteen, Asad Freihat, Mohammed Al-Smadi et al.This analysis proposes an analytical-numerical approach for providing solutions of a class of nonlinear fractional Klein-Gordon equation subjected to appropriate initial conditions in Caputo sense by using the Fractional Reduced Differential Transform Method (FRDTM). This technique provides the solutions very accurately and efficiently in convergent series formula with easily computable coefficients. The behavior of the approximate series solution for different … …Journal of Mathematics and Statistics, Vol. 12, Issue 1 · 26 Mar 2016 · 7,907 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleLOCAL FRACTIONAL VARIATIONAL ITERATION METHOD FOR SOLVING VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITHIN LOCAL FRACTIONAL OPERATORSAmmar Ali NeamahThe paper uses the Local fractional variational Iteration Method for solving the second kind Volterra integro-differential equations within the local fractional integral operators. The analytical solutions within the non-differential terms are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems for the integral equations. …Journal of Mathematics and Statistics, Vol. 10, Issue 3 · 9 Oct 2014 · 6,516 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleExistence Results for a Class of Nonlinear Hadamard Fractional with p-Laplacian Operator Differential EquationsSamah HorrigueIn this study, we are concerned with the existence and uniqueness of solution for some nonlinear Hadamard fractional differential equations. Our results are based on different classical fixed point theorems. Some useful examples are presented in order to illustrate the validity of our main results. …Journal of Mathematics and Statistics, Vol. 17, Issue 1 · 2 Oct 2021 · 6,892 accessesView PDFCite
Research ArticleOpen accessIn the keywordsCoupled Pettis-Hadamard Fractional Differential Systems with Retarded and Advanced ArgumentsSaïd Abbas, Mouffak Benchohra, Seenith SivasundaramIn this study, we present some results concerning the existence of weak solutions for some coupled systems of Hadamard fractional differential equations involving the both retarded and advanced arguments. Our results are obtained by using fixed point theory and the technique of measure of weak noncompactness. …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 10 Feb 2018 · 7,492 accessesView PDFCite
Research ArticleOpen accessIn the keywordsSome Contributions to the Theory of Abstract Degenerate Volterra Integro-Differential EquationsMarko KostićIn this study, we contribute to the existing theory of abstract degenerate Volterra integro-differential equations in sequentially complete locally convex spaces. We investigate a class of abstract degenerate Volterra inclusions by using the multivalued linear operator approach, as well as a class of abstract degenerate multi-term fractional differential equations with Caputo derivatives by using the pure Laplace transform techniques. …Journal of Mathematics and Statistics, Vol. 12, Issue 2 · 17 Jun 2016 · 7,411 accessesView PDFCite
Research ArticleOpen accessIn the abstractOn Almost Periodic Solutions of Abstract Semilinear Fractional Inclusions with Weyl-Liouville Derivatives of Order γ ∈ (0, 1]Marko KostićThe main aim of this paper is to examine the existence and uniqueness of almost periodic solutions for a class of (semilinear) fractional relaxation inclusions with Stepanov almost periodic coefficients. We deal with the Weyl-Liouville fractional derivatives of order γ ∈ (0, 1], paying special attention to the analysis of semilinear differential inclusions of first order. We use the results … …Journal of Mathematics and Statistics, Vol. 13, Issue 3 · 26 Jul 2017 · 6,792 accessesView PDFCite
Research ArticleOpen accessIn the abstractAn Approximate Formula of European Option for Fractional Stochastic Volatility Jump-Diffusion ModelP. Sattayatham, A. IntarasitProblem statement: We presented option pricing when the stock prices follows a jumpdiffusion model and their stochastic volatility follows a fractional stochastic volatility model. This proposed model exhibits the a memory of a stochastic volatility model that is not expressed in the classical stochastic volatility model. Approach: We introduce an approximated method to fractional stochastic volatility model perturbed by the … …Journal of Mathematics and Statistics, Vol. 7, Issue 3 · 27 Jul 2011 · 7,971 accessesView PDFCite