Mittag-Leffler Functions, Related Topics and Applications

by Rudolf Gorenflo, Anatoly A. Kilbas, Francesco Mainardi, Sergei Rogosin

Overview

As a result of researchers’ and scientists’ increasing interest in pure as well as applied mathematics in non-conventional models, particularly those using fractional calculus, Mittag-Leffler functions have recently caught the interest of the scientific community. Focusing on the theory of the Mittag-Leffler functions, the present volume offers a self-contained, comprehensive treatment, ranging from rather elementary matters to the latest research results. In addition to the theory the authors devote some sections of the work to the applications, treating various situations and processes in viscoelasticity, physics, hydrodynamics, diffusion and wave phenomena, as well as shastics. In particular the Mittag-Leffler functions allow us to describe phenomena in processes that progress or decay too slowly to be represented by classical functions like the exponential function and its successors. The book is intended for a broad audience, comprising graduate students, university instructorsand scientists in the field of pure and applied mathematics, as well as researchers in applied sciences like mathematical physics, theoretical chemistry, bio-mathematics, theory of control and several other related areas.

Product Details

ISBN-13:	9783662615508
Publisher:	Springer-Verlag New York, LLC
Publication date:	10/27/2020
Series:	Springer Monographs in Mathematics
Sold by:	Barnes & Noble
Format:	eBook
File size:	49 MB
Note:	This product may take a few minutes to download.

About the Author

R. Gorenflo. In 1960, he received his doctorate in Karlsruhe for work on entire transcendental functions. Starting in 1974 he served as a Professor at the Free University Berlin, where he retired in 1998, remaining an active researcher. Since the 1960s he has been actively interested in fractional integral equations and diffusion problems, leading him to a close collaboration with F. Mainardi and other researchers, focusing on fractional differential equations and related special functions, with a particular emphasis on modeling physical processes. His list of publications comprises more than 170 research articles and two monographs.

A.A. Kilbas (1948-2010). Graduated at the Belarusian State University in Minsk in 1971, where he received his PhD and Doctor of Sciences degrees before becoming a Professor. A.A. Kilbas was a world-known scientist whose contributions to the theory of integral equations, fractional integro-differentiation, fractional differential equations, integral transforms and special functions are highly regarded by the mathematical community. He was the author of more than 300 research articles and 6 monographs.

F. Mainardi. In 1966 he graduated with a degree in Theoretical Physics from the University of Bologna, where he took an advanced degree and continues to serve as a Professor of Mathematical Physics. He is the author of two books, has served as the editor of several compilations and has produced more than 150 research articles in Applied Mathematics, Continuum Mechanics, Wave Motion, Fractional Calculus and Shastic Processes.

S.V. Rogosin. Graduated from the Belarusian State University in Minsk in 1974, where he later received his PhD. His research interests concern boundary value problems, complex analysis, integral equations and fractional calculus and their applications in continuous media mechanics. He is the author of two books, more than 100 research papers, has been the co-organizer of several international conferences and the editor of various compilations.

Table of Contents

Preface.- Introduction.- Overview on the Mittag-Leffler funtion.- Classical Mittag-Laffler function.- Two-parametric Mittag-Leffler functions with three parameters.- Multi-index and multi-variable Mittag-Leffler functions. - The Classical Wright function. - Applications to solution of fractional order equations. - Applications to deterministic models.- Applications to stochastic models. - Appendix A. The Eulerian functions.- Appendix B. Basic of Entire Functions.- Appendix C. Integral transforms.- Appendix D.  Mellin-Barnes integral. - Appendix E. Elements of Fractional Calculus.- Appendix F. Higher transcendental functions.- References.- Index.