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A robust computational analysis of residual power series involving general transform to solve fractional differential equations

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  • Khirsariya, Sagar R.
  • Chauhan, Jignesh P.
  • Rao, Snehal B.

Abstract

In this paper, we provide a new semi-analytical approach, General Residual Power Series Method (GRPSM), to solve fractional differential equations (FDEs). This technique is simple and effective for finding an accurate and approximate solution to linear and nonlinear FDEs. Furthermore, the graphical and numerical results are described in various fractional orders. The solution obtained by GRPSM is compared with Adomian decomposition and Homotopy analysis transform method. We have solved fractional ordered gas dynamics equations and drainage equations using GRPSM, to show the applicability and simplicity of this method.

Suggested Citation

  • Khirsariya, Sagar R. & Chauhan, Jignesh P. & Rao, Snehal B., 2024. "A robust computational analysis of residual power series involving general transform to solve fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 216(C), pages 168-186.
    • Handle: RePEc:eee:matcom:v:216:y:2024:i:c:p:168-186
    DOI: 10.1016/j.matcom.2023.09.007
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    References listed on IDEAS

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    1. Alquran, Marwan & Yousef, Feras & Alquran, Farah & Sulaiman, Tukur A. & Yusuf, Abdullahi, 2021. "Dual-wave solutions for the quadratic–cubic conformable-Caputo time-fractional Klein–Fock–Gordon equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 62-76.
    2. Jagdev Singh & Devendra Kumar & A. Kılıçman, 2013. "Homotopy Perturbation Method for Fractional Gas Dynamics Equation Using Sumudu Transform," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, February.
    3. Omar Abu Arqub & Ahmad El-Ajou & A. Sami Bataineh & I. Hashim, 2013. "A Representation of the Exact Solution of Generalized Lane-Emden Equations Using a New Analytical Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, July.
    4. Khirsariya, Sagar R. & Rao, Snehal B. & Chauhan, Jignesh P., 2023. "A novel hybrid technique to obtain the solution of generalized fractional-order differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 272-290.
    5. Eriqat, Tareq & El-Ajou, Ahmad & Oqielat, Moa'ath N. & Al-Zhour, Zeyad & Momani, Shaher, 2020. "A New Attractive Analytic Approach for Solutions of Linear and Nonlinear Neutral Fractional Pantograph Equations," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    6. Omar Abu Arqub & Zaer Abo-Hammour & Ramzi Al-Badarneh & Shaher Momani, 2013. "A Reliable Analytical Method for Solving Higher-Order Initial Value Problems," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-12, December.
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