Exponential Stability of Higher-Order Fractional Neutral Stochastic Differential Equation via Integral Contractors

Abstract

The existence, uniqueness, and exponential stability results for mild solutions to the fractional neutral stochastic differential system are presented in this article. To demonstrate the results, the concept of bounded integral contractors is combined with the stochastic result and sequencing technique. In contrast to previous publications, we do not need to specify the induced inverse of the controllability operator to prove the stability results, and the relevant nonlinear function does not have to meet the Lipschitz condition. Furthermore, exponential stability results for neutral stochastic differential systems with Poisson jump have been established. Finally, an application to demonstrate the acquired results is discussed. This paper extends the work of Chalishajar et al. \cite{r4} and Renu Chaudhary et al. \cite{r3}.