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We present a series of results focused on the decay in time of solutions ofclassical and anomalous diffusive equations in a bounded domain. The size ofthe solution is measured in a Lebesgue space, and the setting comprisestime-fractional and space-fractional equations and operators of nonlinear type.We also discuss how fractional operators may affect long-time asymptotics.

Decay estimates in time for classical and anomalous diffusion