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Numerical solution of the nonlinear conformable space–time fractional partial differential equations

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  • H. Çerdik Yaslan

    (Pamukkale University)

Abstract

In this paper, a numerical approach for solving the nonlinear space-time fractional partial differential equations with variable coefficients is proposed. The fractional derivatives are described in the conformable sense. The numerical approach is based on shifted Chebyshev polynomials of the second kind and finite difference method. The proposed scheme reduces the main problem to a system of nonlinear algebraic equations. The validity and the applicability of the proposed technique are shown by numerical examples.

Suggested Citation

  • H. Çerdik Yaslan, 2021. "Numerical solution of the nonlinear conformable space–time fractional partial differential equations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(2), pages 407-419, June.
    • Handle: RePEc:spr:indpam:v:52:y:2021:i:2:d:10.1007_s13226-021-00057-0
    DOI: 10.1007/s13226-021-00057-0
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    References listed on IDEAS

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    1. Dehestani, H. & Ordokhani, Y. & Razzaghi, M., 2018. "Fractional-order Legendre–Laguerre functions and their applications in fractional partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 433-453.
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    4. Nagy, A.M., 2017. "Numerical solution of time fractional nonlinear Klein–Gordon equation using Sinc–Chebyshev collocation method," Applied Mathematics and Computation, Elsevier, vol. 310(C), pages 139-148.
    5. Yusuf, Abdullahi & Inc, Mustafa & Isa Aliyu, Aliyu & Baleanu, Dumitru, 2018. "Efficiency of the new fractional derivative with nonsingular Mittag-Leffler kernel to some nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 220-226.
    6. Sweilam, N.H. & Nagy, A.M. & El-Sayed, Adel A., 2015. "Second kind shifted Chebyshev polynomials for solving space fractional order diffusion equation," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 141-147.
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    8. Thabet, Hayman & Kendre, Subhash, 2018. "Analytical solutions for conformable space-time fractional partial differential equations via fractional differential transform," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 238-245.
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