COMPLETELY MONOTONE MULTINOMIAL MITTAG-LEFFLER TYPE FUNCTIONS AND DIFFUSION EQUATIONS WITH MULTIPLE TIME-DERIVATIVES

被引：33
作者：
Bazhlekova, Emilia [1 ]
机构：
[1] Bulgarian Acad Sci, Inst Math & Informat, Acad G Bontchev Str,Block 8, Sofia 1113, Bulgaria
来源：
FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2021年 / 24卷 / 01期
关键词：
multi-term time-fractional diffusion equation; multinomial Mittag-Leffler function; Prabhakar function; completely mono-tone function; complete Bernstein function; FRACTIONAL DIFFUSION; TERM; CALCULUS; FINITE;
D O I：
10.1515/fca-2021-0005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
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页码：88 / 111
页数：24
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