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Mittag-Leffler Functions, Related Topics and Applications / by Rudolf Gorenflo, Anatoly A. Kilbas, Francesco Mainardi, Sergei Rogosin.

Gorenflo, Rudolf.; Kilbas, Anatoly A, author.; Mainardi, Francesco, author.; Rogosin, Sergei, author.
2020
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Title
Mittag-Leffler Functions, Related Topics and Applications / by Rudolf Gorenflo, Anatoly A. Kilbas, Francesco Mainardi, Sergei Rogosin.
Author
Gorenflo, Rudolf.
Edition
2nd ed. 2020.
ISBN
9783662615508
3662615509
3662615495
9783662615492
Published
Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2020.
Language
English
Description
1 online resource.
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.-- Provided by publisher.
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Access limited to authorized users.
Added Author
Kilbas, Anatoly A, author.
Mainardi, Francesco, author.
Rogosin, Sergei, author.
Series
Springer monographs in mathematics, 1439-7382
Available in Other Form
Print version: 9783662615492
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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.

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