Finite-time stability of nonlinear stochastic $ \psi $-Hilfer fractional systems with time delay

Abstract

<abstract><p>In this paper, we study the finite time stability of stochastic $ \psi $-Hilfer fractional-order time-delay systems. Under the stochastic analysis techniques and the generalized Gronwall's inequality for $ \psi $-fractional derivative, the criterion of finite time stability of the solution for nonlinear stochastic $ \psi $-Hilfer fractional systems with time delay is obtained. An example is provided to illustrate the effectiveness of the proposed methods. Some known results in the literature are extended.</p></abstract>