ORIGINAL RESEARCH article
Front. Appl. Math. Stat.
Sec. Dynamical Systems
Volume 11 - 2025 | doi: 10.3389/fams.2025.1608177
Hyers-Ulam, Rassias, and Mittag-Leffler Stability for Quantum Difference Equations in β-Calculus
Provisionally accepted
- 1Carthage University, Tunis, Tunisia
- 2Shaqra University, Kingdom of Saudi Arabia, Shaqra, Riyadh, Saudi Arabia
- 3College of Engineering in Al-Qunfudhah, Umm al-Qura University, Mecca, Saudi Arabia
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This paper investigates first-order nonlinear quantum difference equations governed by a general $\beta$-difference operator, encompassing the Jackson $q$-difference and Hahn difference operators as special cases. We establish sufficient conditions for the existence and uniqueness of solutions using fixed-point theory and examine their solvability under specific assumptions to ensure well-posedness. Particular attention is given to various notions of stability, including Hyers-Ulam, Hyers-Ulam-Rassias, and Mittag-Leffler type stability. Under suitable Lipschitz conditions, we derive explicit error bounds characterizing each type of stability, with Mittag-Leffler stability demonstrated to be of exponential order $\alpha$. Several illustrative examples are included to validate the theoretical findings within the framework of quantum calculus and discrete dynamical systems.
Keywords: Nonlinear quantum difference equations, quantum calculus, Hyers-Ulam stability, Generalized Hyers-Ulam stability, Hyers-Ulam-Rassias stability, Mittag-Leffler stability, Banach fixed point theorem
Received: 08 Apr 2025; Accepted: 25 Apr 2025.
Copyright: © 2025 Chniti, Almutairi and ALZAHRANI. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Chokri Chniti, Carthage University, Tunis, Tunisia
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