We consider a problem which describes the heat diffusion in a complex media with fading memory. The model involves a fractional time derivative of order between zero and one instead of the classical first order derivative. The model takes into account also the effect of a neutral delay. We discuss the existence and uniqueness of a mild solution as well as a classical solution. Then, we prove a Mittag-Leffler stability result. Unlike the integer-order case, we run into considerable difficulties when estimating some problematic terms. It is found that even without the memory term in the heat flux expression, the stability is still of Mittag-Leffler type.

我们考虑一个描述具有记忆衰退的复杂介质中的热扩散问题。该模型涉及零到一阶的分数时间导数，而不是经典的一阶导数。该模型还考虑了中性延迟的影响。我们讨论温和解和经典解的存在性和唯一性。然后，我们证明了 Mittag-Leffler 稳定性结果。与整数阶情况不同，我们在估计一些有问题的项时遇到了相当大的困难。研究发现，即使热流表达式中没有记忆项，其稳定性仍然是Mittag-Leffler 型。