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.

中文翻译：

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具有Mittag-Leffler核的与物理相关的可变阶时间分数反应扩散模型

众所周知，采用Mittag-Leffler核的时间分数反应扩散模型的适定性通常需要对初始数据进行非物理约束。在本文中，我们提出了一个具有Mittag-Leffler核的变阶时间分数阶反应扩散方程，并证明了可以通过在初始时间施加可变分数阶整数限制来消除上述约束，这在数学上证明了可变顺序修改的物理相关性。