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      Approximate solutions for solving nonlinear variable-order fractional Riccati differential equations

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          Abstract

          In this manuscript, we introduce a spectral technique for approximating the variable-order fractional Riccati equation (VO-FRDEs). Firstly, the solution and its space fractional derivatives is expanded as shifted Chebyshev polynomials series. Then we determine the expansion coefficients by reducing the VO-FRDEs and its conditions to a system of algebraic equations. We show the accuracy and applicability of our numerical approach through four numerical examples.

          Most cited references33

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          Applications of Fractional Calculus in Physics

          R. Hilfer (2000)
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            Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term

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              Integration and differentiation to a variable fractional order

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                Author and article information

                Journal
                Nonlinear Analysis: Modelling and Control
                Vilnius University Press
                1392-5113
                February 01 2019
                February 01 2019
                : 24
                : 2
                : 176-188
                Affiliations
                [1 ]Cairo University
                [2 ]Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University; Department of Mathematics, Faculty of Science, Beni-Suef University
                [3 ]Department of Basic Science, Institute of Engineering, Canadian International College (CIC), Giza, Egypt
                [4 ]Department of Mathematics, Cankaya University; Institute of Space Sciences, Magurele-Bucharest, Romania
                Article
                10.15388/NA.2019.2.2
                4e9dd56c-074d-490f-bb10-90913961cd17
                © 2019

                All content is freely available without charge to users or their institutions. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission of the publisher or the author. Articles published in the journal are distributed under a http://creativecommons.org/licenses/by/4.0/.

                History

                Linguistics & Semiotics,Social & Behavioral Sciences,Law,Mathematics,History,Philosophy

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