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

Zhenyu Bai and Chuanzhi Bai ()
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Zhenyu Bai: XJTLU Wisdom Lake Academy of Pharmacy, Xi’an Jiaotong-Liverpool University, Suzhou 215123, China
Chuanzhi Bai: Department of Mathematics, Huaiyin Normal University, Huaian 223300, China

Mathematics, 2024, vol. 12, issue 6, 1-14

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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