We consider a fractional derivative with order varying in time. Then, we derive for it a Leibniz' inequality and an integration by parts formula. We also study an initial value problem with our time variable order fractional derivative and present a regularity result for it, and a study on the asymptotic behavior.

中文翻译：

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时变阶次扩散分数初值问题

我们考虑阶次随时间变化的分数阶导数。然后，我们为其推导出莱布尼茨不等式和分部积分公式。我们还研究了我们的时间变量阶分数阶导数的初值问题，并给出了它的规律性结果，以及对渐近行为的研究。