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The existence and Ulam–Hyers stability results for \(\psi \)-Hilfer fractional integrodifferential equations

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Abstract

We establish sufficient conditions for the existence and uniqueness of solutions for a class of nonlinear fractional integrodifferential equations with boundary conditions involving \(\psi \)-Hilfer fractional derivative of order \(0<\alpha <1 \) and type \(0\le \beta \le 1\). Different types of Ulam–Hyers stability for solutions of the given problem are also discussed. The desired results are proved in weighted spaces with the aid of fixed point theorems due to Schauder, Schaefer and Banach together with generalized Gronwall inequality. Examples illustrating the obtained results are presented.

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Acknowledgements

The authors thank the reviewer for his/her useful suggestions that led to the improvement of the original manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Hodeidah University, Al-Hodeidah, Yemen

    Mohammed S. Abdo

  2. Department of Mathematics, Aden University, Aden, Yemen

    Sabri T. M. Thabet

  3. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Bashir Ahmad

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  1. Mohammed S. Abdo
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  2. Sabri T. M. Thabet
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  3. Bashir Ahmad
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Correspondence to Mohammed S. Abdo.

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Abdo, M.S., Thabet, S.T.M. & Ahmad , B. The existence and Ulam–Hyers stability results for \(\psi \)-Hilfer fractional integrodifferential equations. J. Pseudo-Differ. Oper. Appl. 11, 1757–1780 (2020). https://doi.org/10.1007/s11868-020-00355-x

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  • DOI: https://doi.org/10.1007/s11868-020-00355-x

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