Books in Fractional Calculus

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Kenneth S. Miller, Bertram Ross "An Introduction to the Fractional Calculus and Fractional Differential Equations"
John Wiley & Sons | 1993-05-19 | ISBN: 0471588849 | 384 pages | Djvu | 1,9 MB

This study aims to make the solution of certain integral equations simpler to visualize. It presents material in a methodical manner and includes a bibliography covering references on the development of the subject from 1695 to modern times.

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J. Sabatier, O. P. Agrawal, J. A. Tenreiro Machado “Advances in Fractional Calculus:
Theoretical Developments and Applications in Physics and Engineering"
Springer | 2007-08-24 | ISBN:1402060416 | PDF | 552 pages | 7,6 Mb

In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. Similar progress has been made in other fields listed here. The scope of the book is thus to present the state of the art in the study of fractional systems and the application of fractional differentiation.

As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians.

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Fractional Statistics And Quantum Theory
Publisher: World Scientific | Pages: 300 | 2005-02-28 | ISBN: 9812561609 | PDF | 12 MB

This book explains the subtleties of quantum statistical mechanics in lower dimensions and their possible ramifications in quantum theory. The discussion is at a pedagogical level and is addressed to both graduate students and advanced researchers with a reasonable background in quantum and statistical mechanics. Topics in the first part of the book include the flux tube model of anyons, the braid group and a detailed discussion about the various aspects of quantum and statistical mechanics of a noninteracting anyon gas. The second part of the book includes a detailed discussion about fractional statistics from the point of view of Chern-Simons theories. Topics covered here include Chern-Simons field theories, charged vortices, anyon superconductivity and the fractional quantum Hall effect. Since the publication of the first edition of the book, an exciting possibility has emerged, that of quantum computing using anyons. A section has therefore been included on this topic in the second edition. In addition, new sections have been added about scattering of anyons with hard disk repulsion as well as fractional exclusion statistics and negative probabilities.


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