On stability and regularity for subdiffusion equations involving delays

We study a class of nonlocal evolution equations involving time-varying delays which is employed to depict subdiffusion processes. The global solvability, stability and regularity are shown by using the resolvent theory, nonlocal Halanay inequality, fixed point argument and embeddings of fractional Sobolev spaces. Our result is applied to the nonlocal Fokker–Planck model with nonlinear force fields.