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Existence Results and Ulam–Hyers Stability for a Fully Coupled System of Nonlinear Sequential Hilfer Fractional Differential Equations and Integro-Multistrip-Multipoint Boundary Conditions

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Abstract

In this paper, we investigate the existence of solutions for a new coupled system of sequential Hilfer fractional differential equations equipped with coupled integro-multistrip-multipoint boundary conditions. We make use of the incomplete gamma function to evaluate the integrals involved in the solution of the problem. The uniqueness result for the given problem is obtained by the Banach contraction mapping principle, while the existence results are established with the aid of Krasnosel’skiĭ’s fixed point theorem and Leray–Schauder nonlinear alternative under different assumptions. We also discuss the Ulam–Hyers stability for the problem at hand. Numerical examples are constructed for the illustration of the abstract results.

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Acknowledgements

The Deanship of Scientific Research (DSR) at King Abdulaziz University (KAU), Jeddah, Saudi Arabia has funded this project, under grant no. (KEP-PhD: 35-130-1443). The authors thank the referees for their useful remarks that led to the improvement of the original manuscript.

Funding

The Deanship of Scientific Research (DSR) at King Abdulaziz University (KAU), Jeddah, Saudi Arabia has funded this project, under grant no. (KEP-PhD: 35-130-1443).

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Authors and Affiliations

  1. Department of Mathematics, Texas A &M University, Kingsville, TX, 78363-8202, USA

    Ravi P. Agarwal

  2. 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

    Afrah Assolami, Ahmed Alsaedi & Bashir Ahmad

  3. Department of Mathematical Sciences, Umm Al-Qura University, P.O. Box 14035, Mecca, 21955, Saudi Arabia

    Afrah Assolami

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  1. Ravi P. Agarwal
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  2. Afrah Assolami
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Conceptualization: RA, BA, Methodology: [RA, AA, AA, BA, Formal analysis and investigation: RA, AA, AA, BA, Writing - original draft preparation: RA, AA, AA, BA; Writing - review and editing: RA, AA, AA, BA, Funding acquisition: AA.

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Correspondence to Bashir Ahmad.

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Agarwal, R.P., Assolami, A., Alsaedi, A. et al. Existence Results and Ulam–Hyers Stability for a Fully Coupled System of Nonlinear Sequential Hilfer Fractional Differential Equations and Integro-Multistrip-Multipoint Boundary Conditions. Qual. Theory Dyn. Syst. 21, 125 (2022). https://doi.org/10.1007/s12346-022-00650-6

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