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New discretization of ψ-Caputo fractional derivative and applications

Author

Listed:
  • Pulido, M. Aurora P.
  • Sousa, J. Vanterler C.
  • de Oliveira, E. Capelas

Abstract

In the present paper, two approximations to evaluate the ψ-Caputo fractional derivative are developed using the linear and the quadratic polynomial interpolations. We present a study of the pointwise error for each approximation and illustrate some particular cases that correspond to approximations of the well known fractional derivatives, such as: Caputo, Katugampola and Hadamard fractional derivatives. In order to elucidate the investigated results, we present some examples for each approximation. For concreteness, we show some applications where we solve initial value problems and problems involving fractional sub-diffusion equations. Finally, some concluding remark are presented.

Suggested Citation

  • Pulido, M. Aurora P. & Sousa, J. Vanterler C. & de Oliveira, E. Capelas, 2024. "New discretization of ψ-Caputo fractional derivative and applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 135-158.
    • Handle: RePEc:eee:matcom:v:221:y:2024:i:c:p:135-158
    DOI: 10.1016/j.matcom.2024.02.005
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    References listed on IDEAS

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    1. Chen, Yiming & Ke, Xiaohong & Wei, Yanqiao, 2015. "Numerical algorithm to solve system of nonlinear fractional differential equations based on wavelets method and the error analysis," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 475-488.
    2. Zaky, M.A. & Hendy, A.S. & Suragan, D., 2022. "A note on a class of Caputo fractional differential equations with respect to another function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 289-295.
    3. Ren, Lei & Wang, Yuan-Ming, 2017. "A fourth-order extrapolated compact difference method for time-fractional convection-reaction-diffusion equations with spatially variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 1-22.
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    More about this item

    Keywords

    ψ-Caputo fractional derivative; L1 ψ-Caputo approximation; L1-2 ψ-Caputo approximation; L1 formula; L1-2 formula; Fractional sub-diffusion equations;
    All these keywords.

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance
    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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