Analysis on weighted fractional stochastic delay integro-differential equations

Abstract

With gaussian noise and non-zero initial values ($IV$s), this work investigates the existence of a solution for a weighted stochastic integro fractional infinite delay differential system involving a Riemann-Lioville ($RL$) fractional derivative ($FD$) of order $1/2 < q < 1$. To determine whether a solution exists, we use the fixed point theorem, holder's inequality, fractional calculus, and stochastic analysis approaches. In addition, we present an example to demonstrate our findings.