Ulam stability of Caputo q-fractional delay difference equation: q-fractional Gronwall inequality approach

Abstract

Abstract 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.

Keywords

• Delay difference equation
• q-fractional Gronwall inequality
• Existence
• Uniqueness
• Ulam–Hyers stability
• Ulam–Hyers–Rassias stability