Some results on the study of Caputo–Hadamard fractional stochastic differential equations. (February 2022)

• Record Type: Journal Article
• Authors: Ben Makhlouf, Abdellatif; Mchiri, Lassaad
• Is Part Of: Chaos, solitons and fractals. Volume 155(2022)
• Publication Date: 2022-02
• Subjects: Caputo–Hadamard derivative -- Fractional stochastic differential equations; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2021.111757
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: The existence and uniqueness of global solutions of Caputo–Hadamard fractional stochastic differential equations is studied. The continuity dependence on the initial conditions of solutions of Caputo–Hadamard fractional stochastic differential equations is studied. Novel sufficient conditions are given to guarantee the Ulam–Hyers stability of Caputo–Hadamard fractional stochastic differential equations. Abstract: In this article, we show the existence and uniqueness of solution of Caputo–Hadamardfractional stochastic differential equations (CHFSDE) via the Banach fixed point method (BFPM). We analyze the Ulam–Hyers stability (UHS) of CHFSDE by the generalized and the classical Gronwall inequalities. Two examples are presented to illustrate our results.