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A Hybrid Natural Transform Homotopy Perturbation Method for Solving Fractional Partial Differential Equations

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  • Shehu Maitama

Abstract

A hybrid analytical method for solving linear and nonlinear fractional partial differential equations is presented. The proposed analytical approach is an elegant combination of the Natural Transform Method (NTM) and a well-known method, Homotopy Perturbation Method (HPM). In this analytical method, the fractional derivative is computed in Caputo sense and the nonlinear term is calculated using He’s polynomial. The proposed analytical method reduces the computational size and avoids round-off errors. Exact solution of linear and nonlinear fractional partial differential equations is successfully obtained using the analytical method.

Suggested Citation

  • Shehu Maitama, 2016. "A Hybrid Natural Transform Homotopy Perturbation Method for Solving Fractional Partial Differential Equations," International Journal of Differential Equations, Hindawi, vol. 2016, pages 1-7, September.
    • Handle: RePEc:hin:jnijde:9207869
    DOI: 10.1155/2016/9207869
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    Cited by:

    1. Ya Qin & Adnan Khan & Izaz Ali & Maysaa Al Qurashi & Hassan Khan & Rasool Shah & Dumitru Baleanu, 2020. "An Efficient Analytical Approach for the Solution of Certain Fractional-Order Dynamical Systems," Energies, MDPI, vol. 13(11), pages 1-14, May.
    2. Liaqat, Muhammad Imran & Akgül, Ali, 2022. "A novel approach for solving linear and nonlinear time-fractional Schrödinger equations," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    3. Mamta Kapoor & Nehad Ali Shah & Salman Saleem & Wajaree Weera, 2022. "An Analytical Approach for Fractional Hyperbolic Telegraph Equation Using Shehu Transform in One, Two and Three Dimensions," Mathematics, MDPI, vol. 10(12), pages 1-26, June.

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