Hyers–Ulam Stability of Caputo Fractional Stochastic Delay Differential Systems with Poisson Jumps

Abstract

In this paper, we explore the stability of a new class of Caputo-type fractional stochastic delay differential systems with Poisson jumps. We prove the Hyers–Ulam stability of the solution by utilizing a version of fixed point theorem, fractional calculus, Cauchy–Schwartz inequality, Jensen inequality, and some stochastic analysis techniques. Finally, an example is provided to illustrate the effectiveness of the results.

Keywords

• stochastic fractional delay differential systems
• Hyers–Ulam stability
• fixed point theorem
• stochastic calculus