Weighted fractional stochastic integro-differential equation with infinite delay

In this paper, we consider a weighted fractional stochastic integro-differential equation with infinite delay and nonzero initial values involving a Riemann–Liouville fractional derivative of order 1/2<α<1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1/2<\alpha <1$$\end{document}. The existence of a mild solution is investigated using fractional calculus, stochastic analysis, and the fixed point theorem. An example is also provided to illustrate the obtained result.