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Research Article | Open Access

Analysis of existence and stability in a fractional-order q-difference model

Nihan Turan1( ), Metin Başarır2
Department of Mathematics, Faculty of Arts and Sciences, İstanbul Beykent University, İstanbul 34500, Türkiye
Department of Mathematics, Faculty of Sciences, Sakarya University, Sakarya 54050, Türkiye
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Abstract

In this article, our main aim is to explore the existence and uniqueness of solutions for a fractional-order q-equation under a q-integral boundary condition. Employing well-known fixed point theorems, we derive theoretical findings that advance the theory of q-fractional calculus. An example is provided to show the effectiveness of the results, and the stability of the solutions is discussed.

Keywords

q-calculusCaputo fractional derivativefixed point theoremsUlam-Hyers stabilityUlam-Hyers-Rassias stability

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Electronic Research Archive
Volume 34 Issue 7,
July 2026
Pages 4749-4764
DOI: 10.3934/era.2026209

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Cite this article:
Turan N, Başarır M. Analysis of existence and stability in a fractional-order q-difference model. Electronic Research Archive, 2026, 34(7): 4749-4764. https://doi.org/10.3934/era.2026209

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Received: 06 April 2026
Revised: 16 May 2026
Accepted: 26 May 2026
Published: 15 July 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)