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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2020
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2002.07492 |
| Etiquetas: |
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- 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.