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 map** 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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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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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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DOI: https://doi.org/10.1007/s12346-022-00650-6
Keywords
- Sequential Hilfer fractional differential equations
- Coupled system
- Nonlocal integral-multipoint boundary conditions
- Incomplete gamma function
- Existence
- Fixed point
- Ulam–Hyers stability