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Application of Residual Power Series Method to Fractional Coupled Physical Equations Arising in Fluids Flow

Author

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  • Anas Arafa
  • Ghada Elmahdy

Abstract

The approximate analytical solution of the fractional Cahn-Hilliard and Gardner equations has been acquired successfully via residual power series method (RPSM). The approximate solutions obtained by RPSM are compared with the exact solutions as well as the solutions obtained by homotopy perturbation method (HPM) and q-homotopy analysis method (q-HAM). Numerical results are known through different graphs and tables. The fractional derivatives are described in the Caputo sense. The results light the power, efficiency, simplicity, and reliability of the proposed method.

Suggested Citation

  • Anas Arafa & Ghada Elmahdy, 2018. "Application of Residual Power Series Method to Fractional Coupled Physical Equations Arising in Fluids Flow," International Journal of Differential Equations, Hindawi, vol. 2018, pages 1-10, July.
    • Handle: RePEc:hin:jnijde:7692849
    DOI: 10.1155/2018/7692849
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    Cited by:

    1. Mohammad Alaroud & Abedel-Karrem Alomari & Nedal Tahat & Shrideh Al-Omari & Anuar Ishak, 2023. "A Novel Solution Approach for Time-Fractional Hyperbolic Telegraph Differential Equation with Caputo Time Differentiation," Mathematics, MDPI, vol. 11(9), pages 1-19, May.
    2. Mohammed Kbiri Alaoui & Kamsing Nonlaopon & Ahmed M. Zidan & Adnan Khan & Rasool Shah, 2022. "Analytical Investigation of Fractional-Order Cahn–Hilliard and Gardner Equations Using Two Novel Techniques," Mathematics, MDPI, vol. 10(10), pages 1-19, May.
    3. Az-Zo’bi, Emad A. & Yıldırım, Ahmet & AlZoubi, Wael A., 2019. "The residual power series method for the one-dimensional unsteady flow of a van der Waals gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 188-196.

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