  The motivation that the field of differential equations provide to several
researchers for the challenges that have been challenging them over the decades
has contributed to the strengthening of the area within mathematics. In this
sense, investigating important properties of solutions of differential
equations, in particular fractional, has been object of study due to the
exponential growth of the fractional calculus. In this paper, we investigate
the existence and uniqueness of a new class of mild and strong solution of the
fractional integro-differential equations in the Hilfer fractional derivative
sense in Banach space, by means of the continuously $C_{0}$-semigroup, Banach
fixed point theorem and Gronwall inequality.
