Mittag-Leffler Functions, Related Topics and Applications

Theory and Applications

  • Rudolf Gorenflo
  • Anatoly A. Kilbas
  • Francesco Mainardi
  • Sergei V. Rogosin
Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Rudolf Gorenflo, Anatoly A. Kilbas, Francesco Mainardi, Sergei V. Rogosin
    Pages 1-6
  3. Rudolf Gorenflo, Anatoly A. Kilbas, Francesco Mainardi, Sergei V. Rogosin
    Pages 7-16
  4. Rudolf Gorenflo, Anatoly A. Kilbas, Francesco Mainardi, Sergei V. Rogosin
    Pages 17-54
  5. Rudolf Gorenflo, Anatoly A. Kilbas, Francesco Mainardi, Sergei V. Rogosin
    Pages 55-96
  6. Rudolf Gorenflo, Anatoly A. Kilbas, Francesco Mainardi, Sergei V. Rogosin
    Pages 97-128
  7. Rudolf Gorenflo, Anatoly A. Kilbas, Francesco Mainardi, Sergei V. Rogosin
    Pages 129-164
  8. Rudolf Gorenflo, Anatoly A. Kilbas, Francesco Mainardi, Sergei V. Rogosin
    Pages 165-200
  9. Rudolf Gorenflo, Anatoly A. Kilbas, Francesco Mainardi, Sergei V. Rogosin
    Pages 201-233
  10. Rudolf Gorenflo, Anatoly A. Kilbas, Francesco Mainardi, Sergei V. Rogosin
    Pages 235-268
  11. Back Matter
    Pages 269-443

About this book

Introduction

​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 stochastics. 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 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, theory of control, and several other related areas.

Keywords

33E12, 26A33, 34A08, 45K05, 44Axx, 60G22 Mittag-Leffler functions and generalizations fractional calculus fractional order equations integral transforms mathematical modeling

Authors and affiliations

  • Rudolf Gorenflo
    • 1
  • Anatoly A. Kilbas
    • 2
  • Francesco Mainardi
    • 3
  • Sergei V. Rogosin
    • 4
  1. 1.Free University Berlin Mathematical InstituteBerlinGermany
  2. 2.Belarusian State University Department of Mathematics and MechanicsMinskBelarus
  3. 3.University of Bologna Department of PhysicsBolognaItaly
  4. 4.Belarusian State University Department of EconomicsMinskBelarus

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-43930-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2014
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-662-43929-6
  • Online ISBN 978-3-662-43930-2
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • About this book