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Volume 10
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Article

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

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, Jeddah 21589, Saudi Arabia
*
Author to whom correspondence should be addressed.
Mathematics 2022, 10(5), 767; https://doi.org/10.3390/math10050767
Submission received: 7 February 2022 / Revised: 18 February 2022 / Accepted: 25 February 2022 / Published: 28 February 2022
(This article belongs to the Special Issue Fractional Differential Equations, Inclusions and Inequalities with Applications II)
Versions Notes

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 Caputo fractional (p, q)-difference equations; boundary conditions; existence and uniqueness; 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. Existence and Uniqueness Results for Fractional (p, q)-Difference Equations with Separated Boundary Conditions. Mathematics 2022, 10, 767. https://doi.org/10.3390/math10050767

AMA Style

Neang P, Nonlaopon K, Tariboon J, Ntouyas SK, Ahmad B. Existence and Uniqueness Results for Fractional (p, q)-Difference Equations with Separated Boundary Conditions. Mathematics. 2022; 10(5):767. https://doi.org/10.3390/math10050767

Chicago/Turabian Style

Neang, Pheak, Kamsing Nonlaopon, Jessada Tariboon, Sotiris K. Ntouyas, and Bashir Ahmad. 2022. "Existence and Uniqueness Results for Fractional (p, q)-Difference Equations with Separated Boundary Conditions" Mathematics 10, no. 5: 767. https://doi.org/10.3390/math10050767

APA Style

Neang, P., Nonlaopon, K., Tariboon, J., Ntouyas, S. K., & Ahmad, B. (2022). Existence and Uniqueness Results for Fractional (p, q)-Difference Equations with Separated Boundary Conditions. Mathematics, 10(5), 767. https://doi.org/10.3390/math10050767

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