Fuzzy Mittag–Leffler–Hyers–Ulam–Rassias Stability of Stochastic Differential Equations

Abstract

Stability is the most relevant property of dynamical systems. The stability of stochastic differential equations is a challenging and still open problem. In this article, using a fuzzy Mittag–Leffler function, we introduce a new fuzzy controller function to stabilize the stochastic differential equation (SDE) ν′(γ,μ)=Fγ,μ,ν(γ,μ). By adopting the fixed point technique, we are able to prove the fuzzy Mittag–Leffler–Hyers–Ulam–Rassias stability of the SDE.