Averaging Principle for Caputo Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion with Delays

The aim of this article is to consider a class of neutral Caputo fractional stochastic evolution equations with infinite delay (INFSEEs) driven by fractional Brownian motion (fBm) and Poisson jumps in Hilbert space. First, we establish the local and global existence and uniqueness theorems of mild solutions for the aforementioned neutral fractional stochastic system under local and global Carathéodory conditions by using the successive approximations, stochastic analysis, fractional calculus, and stopping time techniques. The obtained existence result in this article is new in the sense that it generalizes some of the existing results in the literature. Furthermore, we discuss the averaging principle for the proposed neutral fractional stochastic system in view of the convergence in mean square between the solution of the standard INFSEEs and that of the simplified equation. Finally, the obtained averaging theory is validated with an example.

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The Averaging Principle for Hilfer Fractional Stochastic Evolution Equations with Lévy Noise

Yang,

Lv,

Wang

2023

Fractal Fract

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This article focuses on deriving the averaging principle for Hilfer fractional stochastic evolution equations (HFSEEs) driven by Lévy noise. We show that the solutions of the averaged equations converge to the corresponding solutions of the original equations, both in the sense of mean square and of probability. Our results enable us to focus on the averaged system rather than the original, more complex one. Given that the existing literature on the averaging principle for Hilfer fractional stochastic differential equations has been established in finite-dimensional spaces, the novelty here is the derivation of the averaging principle for a class of HFSEEs in Hilbert space. Furthermore, an example is allotted to illustrate the feasibility and utility of our results.

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Averaging Principle for Caputo Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion with Delays

Cited by 5 publications

References 21 publications

Limit behavior of the solution of Caputo-Hadamard fractional stochastic differential equations

Limit behavior of the solution of Caputo-Hadamard fractional stochastic differential equations

Mixed Neutral Caputo Fractional Stochastic Evolution Equations with Infinite Delay: Existence, Uniqueness and Averaging Principle

The Averaging Principle for Hilfer Fractional Stochastic Evolution Equations with Lévy Noise

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