Multidimensional van der Corput-Type Estimates Involving Mittag-Leffler Functions
| Autor: | Berikbol T. Torebek, Michael Ruzhansky |
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| Rok vydání: | 2020 |
| Předmět: |
Mittag-Leffler function
Pure mathematics Applied Mathematics 010102 general mathematics Type (model theory) time-fractional Schrodinger equation 01 natural sciences 010101 applied mathematics Mathematics and Statistics BESSEL 0101 mathematics time-fractional Klein-Gordon equation van der Corput-type estimates Analysis Mathematics |
| Zdroj: | FRACTIONAL CALCULUS AND APPLIED ANALYSIS |
| ISSN: | 1314-2224 1311-0454 |
| DOI: | 10.1515/fca-2020-0082 |
| Popis: | The paper is devoted to study multidimensional van der Corput-type estimates for the intergrals involving Mittag-Leffler functions. The generalisation is that we replace the exponential function with the Mittag-Leffler-type function, to study multidimensional oscillatory integrals appearing in the analysis of time-fractional evolution equations. More specifically, we study two types of integrals with functions E-alpha,E-beta(i lambda phi(x)), x is an element of R-N and E-alpha,E-beta(i(alpha)lambda phi(x)), x is an element of R-N for the various range of alpha and beta. Several generalisations of the van der Corput-type estimates are proved. As an application of the above results, the Cauchy problem for the multidimensional time-fractional Klein-Gordon and time-fractional Schrodinger equations are considered. |
| Databáze: | OpenAIRE |
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