Geodesic
Oscillatory integrals for Mittag--Leffler functions
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 17 (2024) no. 4, pp. 488-496

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Variations of the van der Corput lemmas that involve Mittag-Leffler functions are studied in this paper. The extension involves replacing the exponential function with a Mittag–Leffler-type function. It allows one to analyze oscillatory integrals encountered in the study of time-fractional partial differential equations. Several generalizations of both the first and second van der Corput lemmas are established. Optimal estimates for decay orders in specific cases of Mittag–Leffler functions are also derived.
Keywords: Mittag–Leffler functions, phase function
Mots-clés : amplitude. 
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     title = {Oscillatory integrals for {Mittag--Leffler} functions},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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     publisher = {mathdoc},
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     number = {4},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2024_17_4_a6/}
}
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Akbar R. Safarov; Ulugbek A. Ibragimov. Oscillatory integrals for Mittag--Leffler functions. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 17 (2024) no. 4, pp. 488-496. http://geodesic.mathdoc.fr/item/JSFU_2024_17_4_a6/