Existence and Regularity of Classical Solutions for Integro-Differential Diffusion Equations with Nonlocal Initial Conditions

This paper investigates the existence and regularity of classical solutions to fractional integro-differential equations with nonlocal initial conditions. Considering the integral term, we express the solutions by means of the Laplace transform and a resolvent operator family. We then study the existence and regularity of classical solutions under conditions of weighted uniform boundedness and weighted Hölder continuity conditions, where the weighted continuity conditions are weaker than the traditional Hölder continuity conditions.