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A note on a class of Caputo fractional differential equations with respect to another function

Author

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  • Zaky, M.A.
  • Hendy, A.S.
  • Suragan, D.

Abstract

The mathematical analysis and solutions for a class of ψ-Caputo fractional differential equations are discussed. Assuming that ψ(t) is strictly monotone and armed by the possibility of converting the ψ-Caputo fractional differential equations with respect to another function ψ to its Caputo counterpart by a mapping transformation, the solutions of the ψ-Caputo fractional differential equations can be deduced from the solution representation for the Caputo version via an inverse transformation. We show that the mapping transformation for such derivatives is extremely useful in practical applications. The representation of solutions for constant order time ψ-Caputo fractional diffusion equation and variable order ψ-Caputo fractional mobile-immobile diffusion equation is investigated and the regularity estimates are deduced accordingly.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:196:y:2022:i:c:p:289-295
    DOI: 10.1016/j.matcom.2022.01.016
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    References listed on IDEAS

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    1. Restrepo, Joel E. & Ruzhansky, Michael & Suragan, Durvudkhan, 2021. "Explicit solutions for linear variable–coefficient fractional differential equations with respect to functions," Applied Mathematics and Computation, Elsevier, vol. 403(C).
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    Cited by:

    1. 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.

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