Analysis of a physically-relevant variable-order time-fractional reaction-diffusion model with Mittag-Leffler kernel

It is known that the well-posedness of time-fractional reaction-diffusion models with Mittag-Leffler kernel usually requires non-physical constraints on the initial data. In this paper, we propose a variable-order time-fractional reaction-diffusion equation with Mittag-Leffler kernel and prove that the aforementioned constraints could be eliminated by imposing the integer limit of the variable fractional order at the initial time, which mathematically demonstrates the physically-relevance of the variable-order modifications. (C) 2020 Elsevier Ltd. All rights reserved.