Fractional Evolution Equations with Infinite Time Delay in Abstract Phase Space

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