Mittag-Leffler Functions, Related Topics and Applications
Theory and Applications
Article
Understanding of viscoelastic behaviour of a periodontal membrane under physiological conditions is important for many orthodontic problems. A new analytic model of a nearly incompressible viscoelastic periodo...
Article
The main object of the present paper is to establish new fractional integral formulas (of Marichev-Saigo-Maeda type) involving the products of the multivariable H-functions and the first class of multivariable po...
Article
In this paper, we obtain formulas of fractional integration (of Marichev– Saigo–Maeda type) of the generalized multi-index Mittag-Leffler functions E γ,κ ...
Book
Chapter
Gösta Magnus Mittag-Leffler was born on March 16, 1846, in Stockholm, Sweden. His father, John Olof Leffler, was a school teacher, and was also elected as a member of the Swedish Parliament. His mother, Gust...
Chapter
In this chapter we present the basic properties of the two-parametric Mittag-Leffler function E α, β (z) (see (1.0.3
Chapter
Consider the function defined for \(\alpha _{1},\ \alpha _{2} \in \mathbb{R}\) (α 1 2 +α 2 2 ≠ 0) and \(\beta _{1},\beta _{2} \in \mathbb{C}\) by the series
Chapter
Here we present material illuminating the role of the Mittag-Leffler function and its generalizations in the study of deterministic models. It has already been mentioned that the Mittag-Leffler function is clo...
Chapter
The book is devoted to an extended description of the properties of the Mittag-Leffler function, its numerous generalizations and their applications in different areas of modern science.
Chapter
In this chapter we present the basic properties of the classical Mittag-Leffler function E α (z) (see (1.0.1)). The material can be formally divided into two parts.
Chapter
The Prabhakar generalized Mittag-Leffler function [Pra71] is defined as
Chapter
In this chapter we consider a number of integral equations and differential equations (mainly of fractional order). In representations of their solution, the Mittag-Leffler function, its generalizations and so...
Chapter
This chapter is devoted to the application of the Mittag-Leffler function and related special functions in the study of certain stochastic processes. As this topic is so wide, we restrict our attention to some...
Article
This paper surveys one of the last contributions by the late Professor Anatoly Kilbas (1948–2010) and research made under his advisorship. We briefly describe the historical development of the theory of the di...
Chapter and Conference Paper
The aim of this work is to describe main aspects of the modern theory of fractional differential equations, to present elements of classification of fractional differential equations, to formulate basic compon...
Book and Conference Proceedings
Chapter and Conference Paper
Two-dimensional free boundary value problems are considered. Different models and their connections are discussed. Main attention is paid to the celebrated Hele-Shaw model. Complex-analytic methods are applied...