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Fractal Fract
Volume 5
Issue 4
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Article

Nonlocal Boundary Value Problems of Nonlinear Fractional (p,q)-Difference Equations

by
Pheak Neang
1,
Kamsing Nonlaopon
1,*,
Jessada Tariboon
2,
Sotiris K. Ntouyas
3,4 and
Bashir Ahmad
4
1
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
2
Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
3
Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
4
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
*
Author to whom correspondence should be addressed.
Fractal Fract. 2021, 5(4), 270; https://doi.org/10.3390/fractalfract5040270
Submission received: 8 November 2021 / Revised: 2 December 2021 / Accepted: 7 December 2021 / Published: 10 December 2021
Versions Notes

Abstract

In this paper, we study nonlinear fractional (p,q)-difference equations equipped with separated nonlocal boundary conditions. The existence of solutions for the given problem is proven by applying Krasnoselskii’s fixed-point theorem and the Leray–Schauder alternative. In contrast, the uniqueness of the solutions is established by employing Banach’s contraction mapping principle. Examples illustrating the main results are also presented.
Keywords: Caputo fractional (p,q)-difference equations; nonlocal boundary conditions; existence and uniquness; Leray–Schauder alternative; fixed-point theory Caputo fractional (p,q)-difference equations; nonlocal boundary conditions; existence and uniquness; Leray–Schauder alternative; fixed-point theory

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MDPI and ACS Style

Neang, P.; Nonlaopon, K.; Tariboon, J.; Ntouyas, S.K.; Ahmad, B. Nonlocal Boundary Value Problems of Nonlinear Fractional (p,q)-Difference Equations. Fractal Fract. 2021, 5, 270. https://doi.org/10.3390/fractalfract5040270

AMA Style

Neang P, Nonlaopon K, Tariboon J, Ntouyas SK, Ahmad B. Nonlocal Boundary Value Problems of Nonlinear Fractional (p,q)-Difference Equations. Fractal and Fractional. 2021; 5(4):270. https://doi.org/10.3390/fractalfract5040270

Chicago/Turabian Style

Neang, Pheak, Kamsing Nonlaopon, Jessada Tariboon, Sotiris K. Ntouyas, and Bashir Ahmad. 2021. "Nonlocal Boundary Value Problems of Nonlinear Fractional (p,q)-Difference Equations" Fractal and Fractional 5, no. 4: 270. https://doi.org/10.3390/fractalfract5040270

APA Style

Neang, P., Nonlaopon, K., Tariboon, J., Ntouyas, S. K., & Ahmad, B. (2021). Nonlocal Boundary Value Problems of Nonlinear Fractional (p,q)-Difference Equations. Fractal and Fractional, 5(4), 270. https://doi.org/10.3390/fractalfract5040270

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