From Bessel To Multi-index Mittag-leffler Functions: Enumerable Families, Series In Them And Convergence  
World Scientific | Mathematics | Aug. 25 2016 | ISBN-10: 1786340887 | 228 pages | pdf | 3.18 mb
by Jordanka Paneva-konovska (Author)
                                                

Bessel and Mittag-Leffler functions are prominent withinmathematical and scientific fields due to increasing interest in non-conventional models within applied mathematics. Since the analytical solutions of many differential and integral equations of arbitrary order can be written as series of special functions of fractional calculus, they are now unavoidable tools for handling various mathematical models of integer or fractional order. From Bessel to Multi-Index Mittag-Leffler Functions analyzes this through the study of enumerable families of different classes of special functions.Enumerable families are considered and the convergence of series is investigated. Providing a unified approach to the classical power series, analogues of the classical results for the power series are obtained, and the conclusion is that each of the considered series has a similar convergence behavior to a power series. Also studied are various properties of the Bessel and Mittag-Leffler functions and their generalizations, including estimations, asymptotic formulae, fractional differentiation and integration operators.

Contents:

• Preface
• Acknowledgments
• Introduction
• Bessel Functions and Associated with Them
• Generating Functions of the Bessel and Associated Bessel Functions
• Convergence of Bessel Series
• Bessel and Neumann Expansions
• Completeness of Systems of Bessel and Associated Bessel Functions
• Multi-Index Bessel Functions
• Mittag–Leffler Type Functions
• Latest Generalizations of Both the Bessel and Mittag–Leffler Type Functions
• Series in Mittag–Leffler Type Functions
• Bibliography
• Index