Abstract
In the presented research, the uniqueness and existence of a mild solution for a fractional system of semilinear evolution equations with infinite delay and an infinitesimal generator operator are demonstrated. The generalized Liouville-Caputo derivative of non-integer-order 1 < alpha <= 2 and the parameter 0 < rho < 1 are used to establish our model. The rho-Laplace transform and strongly continuous cosine and sine families of uniformly bounded linear operators are adapted to obtain the mild solution. The Leray-Schauder alternative theorem and Banach contraction principle are used to demonstrate the mild solution's existence and uniqueness in abstract phase space. The results are applied to the fractional wave equation.