Bai, Z.; Bai, C. The Existence and Averaging Principle for Caputo Fractional Stochastic Delay Differential Systems with Poisson Jumps. Axioms2024, 13, 68.
Bai, Z.; Bai, C. The Existence and Averaging Principle for Caputo Fractional Stochastic Delay Differential Systems with Poisson Jumps. Axioms 2024, 13, 68.
Bai, Z.; Bai, C. The Existence and Averaging Principle for Caputo Fractional Stochastic Delay Differential Systems with Poisson Jumps. Axioms2024, 13, 68.
Bai, Z.; Bai, C. The Existence and Averaging Principle for Caputo Fractional Stochastic Delay Differential Systems with Poisson Jumps. Axioms 2024, 13, 68.
Abstract
In this paper, we obtain the existence and uniqueness theorem for solutions of Caputo type fractional stochastic delay differential systems (FSDDSs) with Poisson jumps by utilizing delayed perturbation of Mittag-Leffler function. Moreover, by using Burkholder-Davis-Gundy's inequality, Doob's martingale inequality and Holder inequality, we prove that the solution of the averaged FSDDSs converges to that of the standard FSDDSs in the sense of Lp. Some known results in the literature are extended.
Keywords
Stochastic fractional delay differential systems; Delayed Mittag-Leffler type matrix function; Existence and uniqueness; averaging principle; Lp convergence
Subject
Computer Science and Mathematics, Analysis
Copyright:
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