A new fixed point approach for solutions of a $ p $-Laplacian fractional $ q $-difference boundary value problem with an integral boundary condition

Asghar Ahmadkhanlu; Hojjat Afshari; Jehad Alzabut; Asghar Ahmadkhanlu; Hojjat Afshari; Jehad Alzabut

doi:10.3934/math.20241155

AIMS Mathematics

2024, Volume 9, Issue 9: 23770-23785. doi: 10.3934/math.20241155

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Research article

A new fixed point approach for solutions of a $ p $-Laplacian fractional $ q $-difference boundary value problem with an integral boundary condition

1.
Department of Mathematics, Faculty of Basic Science, Azarbaijan Shahid Madani University, Tabriz, Iran
2.
Department of Mathematics, Faculty of Science, University of Bonab, Bonab, Iran
3.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi Arabia
4.
Department of Industrial Engineering, OSTİM Technical University, Ankara, Türkiye

Received: 27 April 2024 Revised: 29 June 2024 Accepted: 01 July 2024 Published: 08 August 2024
MSC : 34A08, 34Bxx, 34B18

We explored a class of quantum calculus boundary value problems that include fractional $ q $-difference integrals. Sufficient and necessary conditions for demonstrating the existence and uniqueness of positive solutions were stated using fixed point theorems in partially ordered spaces. Moreover, the existence of a positive solution for a boundary value problem with a Riemann-Liouville fractional derivative and an integral boundary condition was examined by utilizing a novel fixed point theorem that included a $ \mathfrak{a} $-$ \eta $-Geraghty contraction. Several examples were provided to demonstrate the efficacy of the outcomes.
- fractional derivatives,
- quantom calculus,
- differential equations,
- boundary value problems,
- positive solution
Citation: Asghar Ahmadkhanlu, Hojjat Afshari, Jehad Alzabut. A new fixed point approach for solutions of a $ p $-Laplacian fractional $ q $-difference boundary value problem with an integral boundary condition[J]. AIMS Mathematics, 2024, 9(9): 23770-23785. doi: 10.3934/math.20241155

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Abstract

We explored a class of quantum calculus boundary value problems that include fractional $ q $-difference integrals. Sufficient and necessary conditions for demonstrating the existence and uniqueness of positive solutions were stated using fixed point theorems in partially ordered spaces. Moreover, the existence of a positive solution for a boundary value problem with a Riemann-Liouville fractional derivative and an integral boundary condition was examined by utilizing a novel fixed point theorem that included a $ \mathfrak{a} $-$ \eta $-Geraghty contraction. Several examples were provided to demonstrate the efficacy of the outcomes.

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