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New Results on the Solvability of Abstract Sequential Caputo Fractional Differential Equations with a Resolvent-Operator Approach and Applications

Author

Listed:
  • Abdelhamid Mohammed Djaouti

    (Department of Mathematics and Statistics, Faculty of Sciences, King Faisal University, Hofuf 31982, Al-Ahsa, Saudi Arabia
    These authors contributed equally to this work.)

  • Khellaf Ould Melha

    (Department of Mathematics, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University, Ouled Fares, Chlef 02180, Algeria
    These authors contributed equally to this work.)

  • Muhammad Amer Latif

    (Department of Mathematics, Faculty of Sciences, King Faisal University, Hofuf 31982, Al-Ahsa, Saudi Arabia)

Abstract

This paper aims to establish the existence and uniqueness of mild solutions to abstract sequential fractional differential equations. The approach employed involves the utilization of resolvent operators and the fixed-point theorem. Additionally, we investigate a specific example concerning a partial differential equation incorporating the Caputo fractional derivative.

Suggested Citation

  • Abdelhamid Mohammed Djaouti & Khellaf Ould Melha & Muhammad Amer Latif, 2024. "New Results on the Solvability of Abstract Sequential Caputo Fractional Differential Equations with a Resolvent-Operator Approach and Applications," Mathematics, MDPI, vol. 12(8), pages 1-18, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1268-:d:1380404
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    References listed on IDEAS

    as
    1. Ahmed Salem & Lamya Almaghamsi, 2023. "Solvability of Sequential Fractional Differential Equation at Resonance," Mathematics, MDPI, vol. 11(4), pages 1-18, February.
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