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Chebyshev spectral method for solving fuzzy fractional Fredholm–Volterra integro-differential equation

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  • Kumar, Sachin
  • Nieto, Juan J.
  • Ahmad, Bashir

Abstract

The fuzzy integral equation is used to model many physical phenomena which arise in many fields like chemistry, physics, and biology, etc. In this article, we emphasize on mathematical modeling of the fuzzy fractional Fredholm–Volterra integral equation. The numerical solution of the fuzzy fractional Fredholm–Volterra equation is determined in which model contains fuzzy coefficients and fuzzy initial condition. First, an operational matrix of Chebyshev polynomial of Caputo type fractional fuzzy derivative is derived in fuzzy environment. The integral term is approximated by the Chebyshev spectral method and the differential term is approximated by the operational matrix. This method converted the given fuzzy fractional integral equation into algebraic equations which are fuzzy in nature. The desired numerical solution is to find out by solving these algebraic equations. The different particular cases of our model have been solved which depict the feasibility of our method. The error tables show the accuracy of the method. We also can see the accuracy of our method by 3D figures of exact and obtained numerical solutions. Hence, our method is suitable to deal with the fuzzy fractional Fredholm–Volterra equation.

Suggested Citation

  • Kumar, Sachin & Nieto, Juan J. & Ahmad, Bashir, 2022. "Chebyshev spectral method for solving fuzzy fractional Fredholm–Volterra integro-differential equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 501-513.
    • Handle: RePEc:eee:matcom:v:192:y:2022:i:c:p:501-513
    DOI: 10.1016/j.matcom.2021.09.017
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    References listed on IDEAS

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    1. Al-Smadi, Mohammed & Arqub, Omar Abu & Zeidan, Dia, 2021. "Fuzzy fractional differential equations under the Mittag-Leffler kernel differential operator of the ABC approach: Theorems and applications," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. A. H. Bhrawy & D. Baleanu & L. M. Assas & J. A. Tenreiro Machado, 2013. "On a Generalized Laguerre Operational Matrix of Fractional Integration," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-7, March.
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    Cited by:

    1. Zhao, Longbin & Wang, Pengde, 2022. "Error estimates of piecewise Hermite collocation method for highly oscillatory Volterra integral equation with Bessel kernel," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 137-150.
    2. Heydari, M.H. & Razzaghi, M., 2023. "Piecewise fractional Chebyshev cardinal functions: Application for time fractional Ginzburg–Landau equation with a non-smooth solution," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).

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