Ulam-Hyers stability results for a novel nonlinear Nabla Caputo fractional variable-order difference system

Abstract

This paper is concerned with a kind of nonlinear Nabla Caputo fractional difference system with variableorder and fixed initial valuable. By applying Krasnoselskii’s fixed point theorem, we give some sufficient conditions to guarantee the existence results for the considered fractional discrete equations. In addition, we further consider the Ulam-Hyers stability by means of generalized Gronwall inequality. At last, two typical examples are delineated to demonstrate the effectiveness of our theoretical results.