Mittag-Leffler Functions, Related Topics and Applications
Theory and Applications
Article
Two integral transforms with kernels generalizing the Macdonald function K u(z) are studied in weighted % MathType!MTE...
Chapter and Conference Paper
The paper is devoted to the study of the integral equation $$ \frac{1}{{\Gamma (\alpha )}}\smallint _a^x{\left( {\frac{u}{x}} \right)^\mu }{\left( {\log \frac{x}{u}} \right)^{\alpha - 1}}f\left( u...
Chapter
The paper is devoted to some aspects of the so-called integral and differential equations of fractional order in which an unknown function is contained under the operation of integration and differentiation of...
Chapter
The paper is devoted to some aspects of differential equations of fractional order and their applications. It is explained a fact that the subject of fractional differential equations is an emergent topic as a...
Article
The paper is devoted to study Map** properties of the Hankel-Schwartz integral transform and the Hankel-Clifford integral transform
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...
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...
Chapter
This 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 \(E_\alpha (z)\) E α ( z ) (see (1.0.1)). The material can be formally divided into two parts. Starting from t...
Chapter
The Prabhakar generalized Mittag-Leffler function [Pra71] is defined where \((\gamma )_n = \gamma (\gamma +1)\ldots (\gamma +n-1)\) ( γ ) n = γ ( γ + 1 ) … ( γ + n - 1 ) (see formula (A.17) in App...
Chapter
This chapter deals with the classical Wright function. Like the functions of Mittag-Leffler type, the functions of Wright type are known to play fundamental roles in various applications of the fractional calc...