Existence and controllability of fractional stochastic neutral functional integro-differential systems with state-dependent delay in Fréchet spaces

This paper investigates the existence and uniqueness of solutions of mild solutions for a fractional stochastic neutral functional integro-differential equation with state-dependent delay in Fréchet spaces. The main techniques rely on the fractional calculus, properties of characteristic solution operators and fixed point theorems. Since we do not assume the characteristic solution operators are compact, our theorems guarantee the effectiveness of controllability results in the infinite dimensional spaces.