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Regularity of solutions to a time-fractional diffusion equation. (English) Zbl 1228.35266

Summary: We prove estimates for the partial derivatives of the solution to a time-fractional diffusion equation posed over a bounded spatial domain. Such estimates are needed for the analysis of effective numerical methods, particularly since the solution is typically less regular than in the familiar case of classical diffusion.

MSC:

35R11 Fractional partial differential equations
35B65 Smoothness and regularity of solutions to PDEs
35C15 Integral representations of solutions to PDEs
35C20 Asymptotic expansions of solutions to PDEs
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