Abstract
This paper deals with the existence and uniqueness of solutions for a nonlinear boundary value problem involving a sequential \(\psi \)-Hilfer fractional integro-differential equations with nonlocal boundary conditions. The existence and uniqueness of solutions are established for the considered problem by using the Banach contraction principle, Sadovski’s fixed point theorem, and Krasnoselskii-Schaefer fixed point theorem due to Burton and Kirk. In addition, the Ulam-Hyers stability of solutions is discussed. Finally, the obtained results are illustrated by examples.
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FH: Actualization, methodology, formal analysis, validation, investigation, initial draft and was a major contributor in writing the manuscript. MES: Actualization, methodology, formal analysis, validation, investigation, software, simulation, initial draft and was a major contributor in writing the manuscript. SR: Actualization, methodology, formal analysis, validation, investigation and initial draft. All authors read and approved the final manuscript.
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Haddouchi, F., Samei, M.E. & Rezapour, S. Study of a sequential \(\psi \)-Hilfer fractional integro-differential equations with nonlocal BCs. J. Pseudo-Differ. Oper. Appl. 14, 61 (2023). https://doi.org/10.1007/s11868-023-00555-1
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DOI: https://doi.org/10.1007/s11868-023-00555-1
Keywords
- \(\psi \)-Hilfer fractional derivative
- Nonlocal conditions
- Existence and uniqueness
- Kuratowski measure of noncompactness
- Stability