Mittag-Leffler Functions, Related Topics and Applications
Theory and Applications
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...
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
Gösta Magnus Mittag- 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.
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
In this chapter we present the basic properties of the two-parametric Mittag-Leffler function \(E_{\alpha ,\beta } (z)\) E α , β ( z ) (see (1.0.3)), which is the most straightforward generalizatio...
Chapter
Consider the function defined for \(\alpha _1,\ \alpha _2\in {\mathbb R}\) α 1 , α 2 ∈ R \((\alpha _1^2+\alpha _2^2\ne 0)\) ( α 1 2 + α 2 2 ≠ 0 ) and \(\beta _1,\beta _2 \in {\mathbb C}\)
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...