Relative Controllability of Caputo Fractional‐Order Stochastic Delay System Driven by Lévy Noise

In this paper, we study the relative controllability of fractional stochastic delay system (FSDS) driven by Lévy noise. First, we derive the solution of linear FSDS by using the delayed Mittag–Leffler matrix function. Then, using Grammian matrix, we discuss the relative controllability of linear FSDS. In addition, the relative controllability of nonlinear FSDS is discussed using the Cauchy–Schwarz inequality, Jensen’s inequality, It’s formula, and Krasnoselskii fixed‐point theorem. Finally, an example is given to verify the theoretical results.