Abstract. We obtain a closed expression for the solution of a linear Volterra integral equation with an additive Hölder continuous noise, which is a fractional Young integral, and with a function as initial condition. This solution is given in terms of the Mittag-Leffler function. Then we study the stability of the solution via the fractional calculus. As an application we analyze the stability in the mean of some stochastic fractional integral equations with a functional of the fractional Brownian motion as an additive noise.
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.MSC: 34A08; 60G22; 26A33; 93D99
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