Hybrid System of Proportional Hilfer-Type Fractional Differential Equations and Nonlocal Conditions with Respect to Another Function

Sotiris K. Ntouyas, Phollakrit Wongsantisuk, Ayub Samadi and Jessada Tariboon ()
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Sotiris K. Ntouyas: Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece
Phollakrit Wongsantisuk: Department of Electronics Engineering Technology, College of Industrial Technology, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
Ayub Samadi: Department of Mathematics, Miyaneh Branch, Islamic Azad University, Miyaneh 5315836511, Iran
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 7, 1-21

Abstract: In this paper, a new class of coupled hybrid systems of proportional sequential ψ -Hilfer fractional differential equations, subjected to nonlocal boundary conditions were investigated. Based on a generalization of the Krasnosel’ski i ˘ ’s fixed point theorem due to Burton, sufficient conditions were established for the existence of solutions. A numerical example was constructed illustrating the main theoretical result. For special cases of the parameters involved in the system many new results were covered. The obtained result is new and significantly contributes to existing results in the literature on coupled systems of proportional sequential ψ -Hilfer fractional differential equations.

Keywords: coupled system; Hilfer fractional proportional derivative; nonlocal conditions; fixed-point theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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