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Bibliographic Details
Main Authors: Ruzhansky, Michael, Torebek, Berikbol T.
Format: Preprint
Published: 2020
Subjects:
Online Access:https://arxiv.org/abs/2002.07492
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Table of Contents:
  • 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.