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Decay estimates for evolutionary equations with fractional time-diffusion. (English) Zbl 1461.35049

Summary: We consider an evolution equation whose time-diffusion is of fractional type, and we provide decay estimates in time for the \(L^s\)-norm of the solutions in a bounded domain. The spatial operator that we take into account is very general and comprises classical local and nonlocal diffusion equations.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35R11 Fractional partial differential equations
26A33 Fractional derivatives and integrals
35K90 Abstract parabolic equations
47J35 Nonlinear evolution equations
58D25 Equations in function spaces; evolution equations
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