Existence and Uniqueness Results for Fractional ( p, q )-Difference Equations with Separated Boundary Conditions

Pheak Neang, Kamsing Nonlaopon, Jessada Tariboon, Sotiris K. Ntouyas and Bashir Ahmad
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Pheak Neang: Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
Kamsing Nonlaopon: Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
Jessada Tariboon: Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
Sotiris K. Ntouyas: Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
Bashir Ahmad: Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Mathematics, 2022, vol. 10, issue 5, 1-15

Abstract: In this paper, we study the existence of solutions to a fractional ( p , q ) -difference equation equipped with separate local boundary value conditions. The uniqueness of solutions is established by means of Banach’s contraction mapping principle, while the existence results of solutions are obtained by applying Krasnoselskii’s fixed-point theorem and the Leary–Schauder alternative. Some examples illustrating the main results are also presented.

Keywords: Caputo fractional ( p , q )-difference equations; boundary conditions; existence and uniqueness; Leray–Schauder alternative; fixed-point theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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