A Result Regarding Finite-Time Stability for Hilfer Fractional Stochastic Differential Equations with Delay

Abstract

Hilfer fractional stochastic differential equations with delay are discussed in this paper. Firstly, the solutions to the corresponding equations are given using the Laplace transformation and its inverse. Afterwards, the Picard iteration technique and the contradiction method are brought up to demonstrate the existence and uniqueness of understanding, respectively. Further, finite-time stability is obtained using the generalized Grönwall–Bellman inequality. As verification, an example is provided to support the theoretical results.

Keywords

• stochastic differential equations
• fractional calculus
• delay
• existence and uniqueness
• finite-time stability