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Numerical Solution of a Nonlinear Fractional Integro-Differential Equation by a Geometric Approach

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Abstract

Numerical solution of a Riemann–Liouville fractional integro-differential boundary value problem with a fractional nonlocal integral boundary condition is studied based on a numerical approach which preserve the geometric structure on the Lorentz Lie group. A fictitious time \(\tau \) is used to transform the dependent variable y(t) into a new one \(u(t,\tau ):=(1+\tau )^{\gamma }y(t)\) in an augmented space, where \(0<\gamma \le 1\) is a parameter, such that under a semi-discretization method and use of a Newton-Cotes quadrature rule the original equation is converted to a system of ODEs in the space \((t,\tau )\) and the obtained system is solved by the Group Preserving Scheme (GPS). Some illustrative examples are given to demonstrate the accuracy and implementation of the method.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran

    S. Shahmorad & S. Pashaei

  2. Department of Mathematics, Basic Science Faculty, University of Bonab, Bonab, Iran

    M. S. Hashemi

Authors
  1. S. Shahmorad
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  2. S. Pashaei
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  3. M. S. Hashemi
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Correspondence to S. Shahmorad.

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Shahmorad, S., Pashaei, S. & Hashemi, M.S. Numerical Solution of a Nonlinear Fractional Integro-Differential Equation by a Geometric Approach. Differ Equ Dyn Syst 29, 585–596 (2021). https://doi.org/10.1007/s12591-017-0395-1

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  • DOI: https://doi.org/10.1007/s12591-017-0395-1

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