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A Numerical Scheme Based on the Chebyshev Functions to Find Approximate Solutions of the Coupled Nonlinear Sine‐Gordon Equations with Fractional Variable Orders

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  • MohammadHossein Derakhshan

Abstract

In this article, a numerical method based on the shifted Chebyshev functions for the numerical approximation of the coupled nonlinear variable‐order fractional sine‐Gordon equations is shown. The variable‐order fractional derivative is considered in the sense of Caputo‐Prabhakar. To solve the problem, first, we obtain the operational matrix of the Caputo‐Prabhakar fractional derivative of shifted Chebyshev polynomials. Then, this matrix and collocation method are used to reduce the solution of the nonlinear coupled variable‐order fractional sine‐Gordon equations to a system of algebraic equations which is technically simpler for handling. Convergence and error analysis are examined. Finally, some examples are given to test the proposed numerical method to illustrate the accuracy and efficiency of the proposed method.

Suggested Citation

  • MohammadHossein Derakhshan, 2021. "A Numerical Scheme Based on the Chebyshev Functions to Find Approximate Solutions of the Coupled Nonlinear Sine‐Gordon Equations with Fractional Variable Orders," Abstract and Applied Analysis, John Wiley & Sons, vol. 2021(1).
    • Handle: RePEc:wly:jnlaaa:v:2021:y:2021:i:1:n:8830727
    DOI: 10.1155/2021/8830727
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    References listed on IDEAS

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    1. Ahmadian, A. & Salahshour, S. & Ali-Akbari, M. & Ismail, F. & Baleanu, D., 2017. "A novel approach to approximate fractional derivative with uncertain conditions," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 68-76.
    2. Heydari, Mohammad Hossein & Avazzadeh, Zakieh, 2018. "Legendre wavelets optimization method for variable-order fractional Poisson equation," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 180-190.
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