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

Nihan Turan; Metin Başarır; Nihan Turan; Metin Başarır

doi:10.3934/era.2026209

Electronic Research Archive

2026, Volume 34, Issue 7: 4749-4764. doi: 10.3934/era.2026209

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Research article

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

Nihan Turan ^{1
,
,},
Metin Başarır ²

1.
Department of Mathematics, Faculty of Arts and Sciences, İstanbul Beykent University, İstanbul 34500, Türkiye
2.
Department of Mathematics, Faculty of Sciences, Sakarya University, Sakarya 54050, Türkiye

Received: 06 April 2026 Revised: 16 May 2026 Accepted: 26 May 2026 Published: 02 June 2026

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.
- $ q $-calculus,
- Caputo fractional derivative,
- fixed point theorems,
- Ulam-Hyers stability,
- Ulam-Hyers-Rassias stability
Citation: Nihan Turan, Metin Başarır. Analysis of existence and stability in a fractional-order $ q $-difference model[J]. Electronic Research Archive, 2026, 34(7): 4749-4764. doi: 10.3934/era.2026209

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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.

References

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