Existence and controllability for conformable fractional stochastic differential equations with infinite delay via measures of noncompactness

In this article, we consider conformable fractional stochastic differential equations (CFSDEs) driven by fBm with infinite delay via measures of noncompactness (MNC). As far as we know, there are few papers considering this issue. First, by virtue of a Monch fixed point theorem and MNC, we explore the existence of solutions for CFSDEs. Subsequently, with the aid of Jensen inequality, Holder inequality, stochastic analysis techniques, and semigroup theory, the controllability for this considered CFSDEs is investigated by employing a Monch fixed point theorem. Thereafter, the controllability of CFSDEs with nonlocal conditions is discussed. Finally, the theoretical result is supported through an example.