Weighted fractional stochastic integro-differential equation with infinite delay

Abstract

Abstract 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 $$1/2<\alpha <1$$ 1 / 2 < α < 1 . 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.

Keywords

• 35A 01
• 60 H 10
• 60 H 20