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On the Laplace integral representation of multivariate Mittag‐Leffler functions in anomalous relaxation |
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| Authors: | Raoul R. Nigmatullin Airat A. Khamzin Dumitru Baleanu |
| Affiliation: | 1. Kazan National Research Technical University (KNRTU‐KAI), Kazan, Tatarstan, Russian Federation;2. Kazan Federal University, Kazan, Tatarstan, Russian Federation;3. Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, Ankara, Turkey;4. Institute of Space Sciences, Magurele‐Bucharest, Romania |
| Abstract: | In the given paper, a special method of representation of the Mittag‐Leffler functions and their multivariate generalizations in the form of the Laplace integrals is suggested. The method is based on the usage of the generalized multiplication Efros theorem. The possibilities of a new method are demonstrated on derivation of the integral representations for relaxation functions used in the anomalous dielectric relaxation in time domain. Copyright © 2016 John Wiley & Sons, Ltd. |
| Keywords: | Mittag‐Leffler functions generalized multiplication efros theorem anomalous dielectric relaxation fractional kinetics laplace transform subclass 65Z05 33F05 |