Demonstrates the relative controllability of fractional stochastic delay systems driven by Lévy noise, suggesting useful mathematical frameworks for control theory.
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.
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Zhong et al. (2026) studied this question.
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