Van der Corput lemmas for Mittag-Leffler functions. I

  • Michael Ruzhansky

    Ghent University, Ghent, Belgium; Queen Mary University of London, London, UK
  • Berikbol T. Torebek

    Ghent University, Ghent, Belgium; Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Van der Corput lemmas for Mittag-Leffler functions. I cover
Download PDF

This article is published open access under our Subscribe to Open model.

Abstract

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 evolution equation are considered.

Cite this article

Michael Ruzhansky, Berikbol T. Torebek, Van der Corput lemmas for Mittag-Leffler functions. I. Z. Anal. Anwend. 43 (2024), no. 3/4, pp. 349–376

DOI 10.4171/ZAA/1763