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Analytical solutions for conformable space-time fractional partial differential equations via fractional differential transform

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  • Thabet, Hayman
  • Kendre, Subhash

Abstract

This paper introduces an efficient fractional differential transform that is called “conformable fractional partial differential transform (CFPDT)” and its properties for solving linear and nonlinear conformable space-time fractional partial differential equations (CSTFPDEs). Moreover, a CFPDT is more practical and helpful for solving abroad CSTFPDEs. Analytical solutions to linear Navier–Stokes equation and nonlinear gas dynamic equations in sense of conformable space-time fractional partial derivatives are successfully obtained to confirm the accuracy and efficiency of the proposed transform.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:109:y:2018:i:c:p:238-245
    DOI: 10.1016/j.chaos.2018.03.001
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    References listed on IDEAS

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    1. Iyiola, O.S. & Tasbozan, O. & Kurt, A. & Çenesiz, Y., 2017. "On the analytical solutions of the system of conformable time-fractional Robertson equations with 1-D diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 1-7.
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    Cited by:

    1. Chaudhary, Manish & Kumar, Rohit & Singh, Mritunjay Kumar, 2020. "Fractional convection-dispersion equation with conformable derivative approach," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. 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.
    3. Li, Mengmeng & Wang, JinRong, 2022. "Existence results and Ulam type stability for conformable fractional oscillating system with pure delay," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    4. Darvishi, M.T. & Najafi, Mohammad & Wazwaz, Abdul-Majid, 2021. "Conformable space-time fractional nonlinear (1+1)-dimensional Schrödinger-type models and their traveling wave solutions," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    5. Ma, Wangrong & Jin, Maozhu & Liu, Yifeng & Xu, Xiaobo, 2019. "Empirical analysis of fractional differential equations model for relationship between enterprise management and financial performance," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 17-23.

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