论文标题
Mittag-Leffler功能的Van der Corput引理。我
Van der Corput lemmas for Mittag-Leffler functions. I
论文作者
论文摘要
在本文中，我们研究了涉及Mittag-Leffler功能的Van der Corput引理的类似物。概括是我们用Mittag-Leffler型函数替换指数函数，以研究出现在时间分数偏微分方程分析中的振荡类型积分。证明了第一和第二范德尔卫式引理的几种概括。还获得了针对Mittag-Leffler功能的特定情况的衰减顺序的最佳估计。作为上述结果的应用，考虑了时间分数Schrödinger方程的广义riemann-lebesgue引理和凯奇问题。
In this paper, we study analogues of the van der Corput lemmas involving Mittag-Leffler functions. The generalisation is that we replace the exponential function with the Mittag-Leffler-type function, to study oscillatory type integrals appearing in the analysis of time-fractional partial differential equations. Several generalisations of the first and second van der Corput lemmas are proved. Optimal estimates on decay orders for particular cases of the Mittag-Leffler functions are also obtained. As an application of the above results, the generalised Riemann-Lebesgue lemma and the Cauchy problem for the time-fractional Schrödinger equation are considered.
