Mittag-Leffler functions, related topics and applications / Rudolf Gorenflo, Anatoly A. Kilbas, Francesco Mainardi, Sergei V. Rogosin.

Format:

Book

Author/Creator:

Gorenflo, Rudolf, author.

Kilbas, A. A. (Anatoliĭ Aleksandrovich), author.

Mainardi, F. (Francesco), 1942- author.

Rogosin, Sergei V., author.

Series:

Springer monographs in mathematics 1439-7382

Springer monographs in mathematics, 1439-7382

Language:

English

Subjects (All):

Fractional calculus.

Integral transforms.

Mathematical models.

Mathematical physics.

Functions, Special.

Integral equations.

Probabilities.

Mathematical Physics.

Special Functions.

Mathematical Modeling and Industrial Mathematics.

Integral Equations.

Probability Theory and Stochastic Processes.

Local Subjects:

Mathematical Physics.

Special Functions.

Mathematical Modeling and Industrial Mathematics.

Integral Equations.

Probability Theory and Stochastic Processes.

Physical Description:

xvi, 540 pages : illustrations ; 25 cm.

Edition:

Second edition.

Place of Publication:

Berlin, Germany : Springer, [2020]

Summary:

The 2nd edition of this book is essentially an extended version of the 1st and provides a very sound overview of the most important special functions of Fractional Calculus. It has been updated with material from many recent papers and includes several surveys of important results known before the publication of the 1st edition, but not covered there. 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 caught the interest of the scientific community. Focusing on the theory of Mittag-Leffler functions, this 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 applications, treating various situations and processes in viscoelasticity, physics, hydrodynamics, diffusion and wave phenomena, as well as stochastics. In particular, the Mittag-Leffler functions make it possible to describe phenomena in processes that progress or decay too slowly to be represented by classical functions like the exponential function and related special functions. The book is intended for a broad audience, comprising graduate students, university instructors and scientists in the field of pure and applied mathematics, as well as researchers in applied sciences like mathematical physics, theoretical chemistry, bio-mathematics, control theory and several other related areas.

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.

Notes:

Includes bibliographical references and index.

ISBN:

9783662615492

3662615495

OCLC:

1225274054

Publisher Number:

Bestellnummer: 978-3-662-61549-2

Bestellnummer: 86956483