Mixed Hilfer and Caputo Fractional Riemann–Stieltjes Integro-Differential Equations with Non-Separated Boundary Conditions

Ayub Samadi, Sotiris K. Ntouyas and Jessada Tariboon ()
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Ayub Samadi: Department of Mathematics, Miyaneh Branch, Islamic Azad University, Miyaneh 5315836511, Iran
Sotiris K. Ntouyas: Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece
Jessada Tariboon: Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand

Mathematics, 2024, vol. 12, issue 9, 1-13

Abstract: In this paper, we investigate a sequential fractional boundary value problem which contains a combination of Hilfer and Caputo fractional derivative operators and non-separated boundary conditions. We establish the existence of a unique solution via Banach’s fixed point theorem, while by applying Leray–Schauder’s nonlinear alternative, we prove an existence result. Finally, examples are provided to demonstrate the results obtained.

Keywords: Hilfer fractional differential derivative; fractional integrals; existence and uniqueness; fixed-point theorems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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