Mild Solutions of Fractional Integrodifferential Diffusion Equations with Nonlocal Initial Conditions via the Resolvent Family

Abstract

Fractional integrodifferential diffusion equations play a significant role in describing anomalous diffusion phenomena. In this paper, we study the existence and uniqueness of mild solutions to these equations. Firstly, we construct an appropriate resolvent family, through which the related equicontinuity, strong continuity, and compactness properties are studied using the convolution theorem of Laplace transform, the probability density function, the Cauchy integral formula, and the Fubini theorem. Then, we construct a reasonable mild solution for the considered equations. Finally, we obtain some sufficient conditions for the existence and uniqueness of mild solutions to the considered equations by some fixed point theorems.