11 Result(s)
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Chapter
Historical Overview of the Mittag-Leffler Functions
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...
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Chapter
The Two-Parametric Mittag-Leffler Function
In this chapter we present the basic properties of the two-parametric Mittag-Leffler function E α, β (z) (see (1.0.3
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Chapter
Multi-index Mittag-Leffler Functions
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
6.1.1 $$\displaystyle{ E_{\alpha _{... -
Chapter
Applications to Deterministic Models
Here we present material illuminating the role of the Mittag-Leffler function and its generalizations in the study of deterministic models. It has already been mentioned that the Mittag-Leffler function is clo...
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Chapter
Introduction
The book is devoted to an extended description of the properties of the Mittag-Leffler function, its numerous generalizations and their applications in different areas of modern science.
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Chapter
The Classical Mittag-Leffler Function
In this chapter we present the basic properties of the classical Mittag-Leffler function E α (z) (see (1.0.1)). The material can be formally divided into two parts.
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Chapter
Mittag-Leffler Functions with Three Parameters
The Prabhakar generalized Mittag-Leffler function [Pra71] is defined as
5.1.1 $$\displaystyle{ E_{\alpha,\beta }^{\gamma }(z):=\sum _{ n=0}^{\infty } \frac{(\gamma )_{n}} {n!\varGamma (\alpha n+\beta )}\,z^... -
Chapter
Applications to Fractional Order Equations
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...
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Chapter
Applications to Stochastic Models
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...
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Chapter and Conference Paper
The Role of S.G. Samko in the Establishing and Development of the Theory of Fractional Differential Equations and Related Integral Operators
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...
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Chapter and Conference Paper
2D Free Boundary Value Problems
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...
