Strong Solutions to Semilinear Subdiffusion Equations With Completely Positive Kernels

We deal with an abstract model of nonlocal evolution equations with completely positive kernels and nonlinear perturbations. By using the subordination principle, we derive a representation and regularity estimates for resolvent family, which allow us to prove a solvability result for the associated Cauchy problem in fractional Sobolev spaces. Then, by using the fixed point argument and the analytic resolvent theory, we are able to demonstrate that the obtained solution is a strong one.