Stability for a class of semilinear fractional stochastic integral equations

TL;DR

This paper develops stability criteria for a class of semilinear fractional stochastic integral equations driven by fractional Brownian motion, using comparison principles and Mittag-Leffler functions.

Contribution

It introduces new stability conditions for fractional stochastic integral equations with additive noise and fractional Brownian motion, expanding the theoretical understanding of their behavior.

Findings

Established mean stability and asymptotic stability criteria.

Derived conditions for global and Mittag-Leffler stability.

Provided comparison results for fractional equations with stochastic terms.

Abstract

In this paper we study some stability criteria for some semilinear integral equations with a function as initial condition and with additive noise, which is a Young integral that could be a functional of fractional Brownian motion. Namely, we consider stability in the mean, asymptotic stability, stability, global stability and Mittag-Leffler stability. To do so, we use comparison results for fractional equations and an equation (in terms of Mittag-Leffler functions) whose family of solutions includes those of the underlying equation.