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Fractional pseudospectral integration/differentiation matrix and fractional differential equations

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  • Gholami, Saeid
  • Babolian, Esmail
  • Javidi, Mohammad

Abstract

In this paper, we present a new pseudospectral integration matrix which can be used to compute n−fold integrals of function f for any n∈R+. Also, it can be used to calculate the derivatives of f for any non-integer order α < 0. We use the Chebyshev interpolating polynomial for f at the Gauss–Lobatto points in [−1,1]. Less computational complexity and programming, much higher rate in running, calculating the integral/derivative of fractional order and its extraordinary accuracy, are advantages of this method in comparison with other known methods. We apply two approaches by using this matrix to solve some fractional differential equations with high accuracy. Some numerical examples are presented.

Suggested Citation

  • Gholami, Saeid & Babolian, Esmail & Javidi, Mohammad, 2019. "Fractional pseudospectral integration/differentiation matrix and fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 314-327.
    • Handle: RePEc:eee:apmaco:v:343:y:2019:i:c:p:314-327
    DOI: 10.1016/j.amc.2018.08.044
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    References listed on IDEAS

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    1. Pirkhedri, A. & Javadi, H.H.S., 2015. "Solving the time-fractional diffusion equation via Sinc–Haar collocation method," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 317-326.
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    Cited by:

    1. Muhammad Ismail & Umer Saeed & Jehad Alzabut & Mujeeb ur Rehman, 2019. "Approximate Solutions for Fractional Boundary Value Problems via Green-CAS Wavelet Method," Mathematics, MDPI, vol. 7(12), pages 1-20, December.
    2. Bonab, Zahra Farzaneh & Javidi, Mohammad, 2020. "Higher order methods for fractional differential equation based on fractional backward differentiation formula of order three," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 71-89.

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