Pseudo almost periodic solutions to integro-differential equations of heat conduction in materials with memory

We investigate the existence of pseudo almost periodic solutions for a class of integro-differential equation with nonlocal initial conditions arising in the study of heat conduction in materials with memory. We first establish some existence theorems for abstract semilinear integro-differential equations with nonlocal initial conditions, and then, we apply our abstract results to the addressed integro-differential equation arising in the study of heat conduction in materials with memory.