From Bessel to multi-index Mittag-Leffler functions. Enumerable families, series in them and convergence (Q2818807)

This book represents a well-organised text on two important families of special functions, namely Bessel functions and Mittag-Leffler functions, and their multi-parametric generalisations.NEWLINENEWLINEThese functions are known in the study of classical problems of analysis and differential equations. More import is that they play important role in fractional calculus and its applications, the topics which became very important in the recent decades.NEWLINENEWLINENEWLINEThe author discusses the following main questions in relation to the classical and generalised functions of Bessel and Mittag-Leffler type, namely, integral representations and convergence, asymptotic behaviour, Tauberian type theorems, completeness of systems of these functions, representations in terms of the generalized Wright function, the Meijer \(G\)- and the Fox \(H\)-functions with special values of parameters. Special attention is paid to the relations of these functions to the problems of fractional calculus.NEWLINENEWLINENEWLINEIn series of the recent articles, the author developed a theory of the multi-index Bessel and Mittag-Leffler functions. These results are presented in the book, too.NEWLINENEWLINENEWLINEThe book can be recommended to those interested to study questions of special functions, fractional calculus and fractional differential equations.