Moment bounds for a class of stochastic nonlinear fractional Volterra integral equations of the second kind

Abstract

This paper studies and compares the second moment (Energy growth) bounds for solutions to a class of stochastic fractional Volterra integral equations of the second kind, under some Lipschitz continuity conditions on the parameters. The result shows that both solutions exhibit exponential growth but at different rates. The existence and uniqueness of the mild solutions are established via the Banach fixed point theorem.