Existence and regularity of solutions to time-fractional diffusion equations

We investigate some initial-boundary value problems for time-fractional diffusion equations of order α∈(0,1). Such equations model anomalous diffusion on fractals. The existence of solution irrelevant to α is established only if the external force function f is weighted Hölder continuous, which is weaker than Hölder continuous. Some interesting versions of maximal and spatial regularity criteria depending on the fractional exponent α are also discussed.