Van der Corput lemmas for Mittag-Leffler functions. I
Ruzhansky M. Torebek B.T.
2024European Mathematical Society Publishing House
Zeitschrift für Analysis und ihre Anwendungen
2024#43Issue 3-4349 - 376 pp.
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.
asymptotic estimate , Mittag-Leffler function , van der Corput lemma
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Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281, Ghent, 9000, Belgium
School of Mathematical Sciences, Queen Mary University of London, London, United Kingdom
Institute of Mathematics and Mathematical Modeling, 28 Shevchenko street, Almaty, 050010, Kazakhstan
Department of Mathematics: Analysis
School of Mathematical Sciences
Institute of Mathematics and Mathematical Modeling
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