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Existence results for nonlinear neutral generalized Caputo fractional differential equations

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Abstract

This paper is devoted to proving some existence and uniqueness of solutions to a category of boundary value problems for a nonlinear neutral generalized Caputo fractional differential equation with generalized Riemann–Liouville integral boundary conditions. We apply a variety assort of fixed point theorems such as Krasnoselskii and Banach. We also establish the Ulam–Hyers stability results for the addressed problem. Further, an example illustrate our acquired results.

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Acknowledgements

The authors thankful the reviewers for their useful comments that improved of the manuscript.

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Authors and Affiliations

  1. Laboratory of Mathematics And Applied Sciences, University of Ghardaia, 47000, Metlili, Algeria

    Naas Adjimi & Abdelatif Boutiara

  2. Department of Mathematics, Hodeidah University, Al-Hudeidah, Yemen

    Mohammed S. Abdo

  3. Laboratory of Mathematics and Applied Sciences, University of Saad, Dahlab Blida 1, 9000, Ouled Yaïch, Algeria

    Maamar Benbachir

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  1. Naas Adjimi
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  2. Abdelatif Boutiara
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  3. Mohammed S. Abdo
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  4. Maamar Benbachir
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Correspondence to Abdelatif Boutiara.

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Adjimi, N., Boutiara, A., Abdo, M.S. et al. Existence results for nonlinear neutral generalized Caputo fractional differential equations. J. Pseudo-Differ. Oper. Appl. 12, 25 (2021). https://doi.org/10.1007/s11868-021-00400-3

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  • DOI: https://doi.org/10.1007/s11868-021-00400-3

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