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An Efficient Numerical Method for Solving a Class of Nonlinear Fractional Differential Equations and Error Estimates

Author

Listed:
  • Xin Song

    (School of Data Science and Engineering, South China Normal University, Shanwei 516600, China)

  • Rui Wu

    (School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China)

Abstract

In this paper, we present an efficient method for solving a class of higher order fractional differential equations with general boundary conditions. The convergence of the numerical method is proved and an error estimate is given. Finally, eight numerical examples, both linear and nonlinear, are presented to demonstrate the accuracy of our method. The proposed method introduces suitable base functions to calculate the approximate solutions and only requires us to deal with the linear or nonlinear systems. Thus, our method is convenient to implement. Furthermore, the numerical results show that the proposed method performs better compared to the existing ones.

Suggested Citation

  • Xin Song & Rui Wu, 2024. "An Efficient Numerical Method for Solving a Class of Nonlinear Fractional Differential Equations and Error Estimates," Mathematics, MDPI, vol. 12(12), pages 1-12, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:12:p:1824-:d:1413240
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    References listed on IDEAS

    as
    1. Hassan Kamil Jassim & Mohammed Abdulshareef Hussein, 2023. "A New Approach for Solving Nonlinear Fractional Ordinary Differential Equations," Mathematics, MDPI, vol. 11(7), pages 1-13, March.
    2. Muhammad Aslam Noor & Syed Tauseef Mohyud-Din, 2008. "Variational Iteration Method for Fifth-Order Boundary Value Problems Using He's Polynomials," Mathematical Problems in Engineering, Hindawi, vol. 2008, pages 1-12, March.
    3. Yousif, Majeed A. & Hamasalh, Faraidun K., 2024. "The fractional non-polynomial spline method: Precision and modeling improvements," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 512-525.
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