Abstract
In this paper, we investigate the Ulam’s stability results for nonlinear Hilfer fractional stochastic differential systems (HFSDS) in finite dimensional stochastic setting. Firstly, by using fractional calculus (generalized fractional derivative), stochastic analysis method and fixed point rout with appropriate hypotheses on nonlinear terms, we prove existence and uniqueness of fixed point for nonlinear HFSDS. Secondly, we study the Ulam-Hyers stability and thereafter, we discuss Ulam-Hyers-Rassias stability results for HFSDS. Finally, an example is presented to illustrate the obtained theory.
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