Decay estimates for evolutionary equations with fractional time-diffusion

TL;DR

This paper derives decay estimates over time for solutions to evolution equations with fractional time-diffusion, applicable to a broad class of spatial operators including local and nonlocal diffusions.

Contribution

It provides general decay estimates for fractional time-diffusion equations with a wide range of spatial operators, extending existing results.

Findings

Decay estimates in time for solutions in bounded domains

Applicable to classical and nonlocal diffusion equations

General framework for fractional time-diffusion equations

Abstract

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.