Mittag-Leffler Functions, Related Topics and Applications. 2nd ed. 2020

種類:

電子ブック

責任表示:

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

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2020

著者名:

• Gorenflo, Rudolf.
• Kilbas, Anatoly A.
• Mainardi, Francesco.
• Rogosin, Sergei.
• SpringerLink (Online service)

シリーズ名:

Springer Monographs in Mathematics ;

ISBN:

9783662615508 [3662615509]    

注記:

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.
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. I

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