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.

The Existence and Averaging Principle for Caputo Fractional Stochastic Delay Differential Systems with Poisson Jumps

“…They provide a powerful framework for understanding and predicting the behavior of complex systems with memory, randomness, and time delays. See, for example, [1][2][3][4][5][6] and the references cited therein.…”

The Existence and Averaging Principle for Caputo Fractional Stochastic Delay Differential Systems with Poisson Jumps

“…They provide a powerful framework for understanding and predicting the behavior of complex systems with memory, randomness, and time delays. See for examples [1][2][3][4][5][6], and the references cited therein.…”