Completely monotone multinomial mittag-leffler type functions and diffusion equations with multiple time-derivatives
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Abstract The multinomial Mittag-Leffler function plays a crucial role in the study of multi-term time-fractional evolution equations. In this work we establish basic properties of the Prabhakar type generalization of this function with the main emphasis on complete monotonicity. As particular examples, the relaxation functions for equations with multiple time-derivatives in the so-called “natural” and “modified” forms are studied in detail and useful estimates are derived. The obtained results extend known properties of the classical Mittag-Leffler function. The main tools used in this work are Laplace transform and Bernstein functions’ technique.
2005 ◽
Vol 46
(11)
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pp. 113512
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2015 ◽
Vol 26
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pp. 737-752
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2020 ◽
Vol 23
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pp. 1663-1677
2020 ◽
Vol 19
(2)
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pp. 285-298
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2004 ◽
Vol 193
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pp. 1671-1692
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2005 ◽
Vol 85
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pp. 65-65
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