On the $\epsilon$-regular mild solution for fractional abstract integro-differential equations

In this present paper, we first obtained some estimates involving parts of $\epsilon$-regular mild solutions of the fractional integro-differential equation. In this sense, through these preliminary results, we investigate the main results of this paper, i.e., the existence, regularity and continuous dependence of $\epsilon$-regular mild solutions for fractional abstract integro-differential equations in Banach space.