Hyers-Ulam and Hyers-Ulam Rassias stability of Caputo fractional Hahn difference equations

​In this paper, we investigate Hyers–Ulam and Hyers–Ulam–Rassias stability for fractional linear Hahn difference equations of Caputo Type. To the best of our knowledge, this is the first work concerning Hyers–Ulam type stability in the framework of Caputo fractional Hahn difference equations, thereby filling a significant gap in the literature on fractional stability theory. Our approach is based on establishing an equivalence between the fractional Hahn difference initial value problem and a corresponding fractional integral equation, via the Caputo–Hahn inversion formula. These results lay a strong groundwork for analyzing the stability of Hahn fractional systems, which could be useful in various scientific and engineering fields. Finally, illustrative examples are given to show the applicability of the theoretical results.