A novel result on averaging principle of stochastic Hilfer-type fractional system involving non-Lipschitz coefficients. (December 2021)

• Record Type: Journal Article
• Authors: Luo, Danfeng; Zhu, Quanxin; Luo, Zhiguo
• Is Part Of: Applied mathematics letters. Volume 122(2021)
• Publication Date: 2021-12
• Subjects: Averaging principle -- Hilfer fractional derivative -- Stochastic differential equations; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2021.107549
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this paper, we investigate a class of stochastic Hilfer-type fractional differential equations (SHFDEs) involving non-Lipschitz coefficients. With the aid of the Laplace transform and its inverse, we derive an implicit solution to the SHFDEs. Subsequently, we present the averaging principle result using Jensen's inequality, the Cauchy–Schwarz inequality, Doob's martingale inequality, and the Grönwall–Bellman inequality. Finally, we solve an example problem numerically to prove the correctness of the theoretical solution.