Finite-time stability of nonlinear stochastic ψ-Hilfer fractional systems with time delay

Abstract

In this paper, we study the finite time stability of stochastic ψ-Hilfer fractional-order time-delay systems. Under the stochastic analysis techniques and the generalized Gronwall's inequality for ψ-fractional derivative, the criterion of finite time stability of the solution for nonlinear stochastic ψ-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.

Keywords

• ψ-hilfer fractional derivative
• generalized gronwall's inequality
• finite time stability