In this article, we discuss the existence and uniqueness of solution of a delay Caputo q-fractional difference system. Based on the q-fractional Gronwall inequality, we analyze the Ulam-Hyers stability and the Ulam-Hyers-Rassias stability. An example is provided to support the theoretical results.
Fractional difference equations have become important due to their qualitative properties and applications in discrete modeling. Stability analysis of solutions is one of the most widely used qualitative properties with tremendous applications. In this paper, we investigate the existence and stability results for a class of non-linear Caputo nabla fractional difference equations. To obtain the existence and stability results, we use Schauder’s fixed point theorem, the Banach contraction principle and Krasnoselskii’s fixed point theorem. The analysis of the theoretical results depends on the structure of nabla discrete Mittag-Leffler functions. An example is provided to illustrate the theoretical results.
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