三变量的 Mittag-Leffler 型函数

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
A. Hasanov, Hilola Yuldashova
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引用次数: 0

摘要

在本文中,我们将米塔格-勒弗勒式函数 、 和 ,分别对应于我们熟悉的劳里切拉三变量超几何函数 、 和 。首先,从最简单形式的 Mittag-Leffler 型函数到我们正在研究的函数,将介绍有关该函数和超几何型函数的发展历史、研究和重要性的必要信息。文章研究的这些三变量 Mittag-Leffler 型函数的各种性质和特征包括:它们与经典 Mittag-Leffler 函数的其他扩展和广义的关系、它们的三维收敛区域、它们的欧拉型积分表示、它们的拉普拉斯变换以及它们与分数微积分的黎曼-刘维尔算子的联系。三变量 Mittag-Leffler 函数与涉及不同分数阶的分数微分方程系统的联系在物理学的某些应用中是必要的,因此,我们提供了与之相关的偏微分方程系统。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Mittag‐Leffler type functions of three variables
In this article, we generalized Mittag‐Leffler‐type functions , and , which correspond, respectively, to the familiar Lauricella hypergeometric functions , and of three variables. Initially, from the Mittag‐Leffler type function in the simplest form to the functions we are studying, necessary information about the development history, study, and importance of this and hypergeometric type functions will be introduced. Among the various properties and characteristics of these three‐variable Mittag‐Leffler‐type function , which we investigate in the article, include their relationships with other extensions and generalizations of the classical Mittag‐Leffler functions, their three‐dimensional convergence regions, their Euler‐type integral representations, their Laplace transforms, and their connections with the Riemann‐Liouville operators of fractional calculus. The link of three‐variable Mittag‐Leffler function with fractional differential equation systems involving different fractional orders is necessary on certain applications in physics.Therefore, we provide the systems of partial differential equations which are associated with them.
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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