© 2013

Fractional Derivatives for Physicists and Engineers

Background and Theory


  • First book combining a clear introduction to the fractional calculus with the description of a wide sphere of physical applications

  • Combined ease of access and breadth of scope

  • Enables readers to apply the new methods in their own research


Part of the Nonlinear Physical Science book series (NPS)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Background

    1. Front Matter
      Pages 1-1
    2. Vladimir V. Uchaikin
      Pages 3-58
    3. Vladimir V. Uchaikin
      Pages 59-106
    4. Vladimir V. Uchaikin
      Pages 107-195
  3. Theory

    1. Front Matter
      Pages 197-197
    2. Vladimir V. Uchaikin
      Pages 199-255
    3. Vladimir V. Uchaikin
      Pages 257-327
    4. Vladimir V. Uchaikin
      Pages 329-381
  4. Back Matter
    Pages 383-385

About this book


The first derivative of a particle coordinate means its velocity, the second means its acceleration, but what does a fractional order derivative mean? Where does it come from, how does it work, where does it lead to? The two-volume book written on high didactic level answers these questions. Fractional Derivatives for Physicists and Engineers— The first volume contains a clear introduction into such a modern branch of analysis as the fractional calculus. The second develops a wide panorama of applications of the fractional calculus to various physical problems. This book recovers new perspectives in front of the reader dealing with turbulence and semiconductors, plasma and thermodynamics, mechanics and quantum optics, nanophysics and astrophysics. 

The book is addressed to students, engineers and physicists, specialists in theory of probability and statistics, in mathematical modeling and numerical simulations, to everybody who doesn't wish to stay apart from the new mathematical methods becoming more and more popular.

Prof. Vladimir V. UCHAIKIN is a known Russian scientist and pedagogue, a Honored Worker of Russian High School, a member of the Russian Academy of Natural Sciences. He is the author of about three hundreds articles and more than a dozen books (mostly in Russian)  in Cosmic ray physics, Mathematical physics, Levy stable statistics, Monte Carlo methods with applications to anomalous processes in complex systems of various levels: from quantum dots to the Milky Way galaxy.


Applications Fractional derivatives Fractals physics HEP Hereditarity NPS Stable statistics fractional differential equations self-similar stochasticity

Authors and affiliations

  1. 1.Ulyanovsk State UniversityUlyanovskRussia

Bibliographic information

Industry Sectors
IT & Software


“The book is addressed to students, engineers, physicists and researchers working in the field of applied analysis and fractional calculus. The book is well written and references are provided at the end of each chapter. Both volumes yield a useful and interesting addition to the literature on fractional calculus.” (S. L. Kalla, zbMATH 1312.26002, 2015)

“The book is a kind of encyclopedia and will be of exceptional value for all researchers engaged in the application of singular integro-differential operators not only in physics and engineering, but also in other sciences such as chemistry, biology, ecology, and geology. … The book will be useful to engineers and physicists and to specialists in mathematical modelling, theory of probability and statistics, and numerical simulations, as well as to anybody interested in mastering the new mathematical methods and finding more and more applications.” (Paulius Miškinis, Mathematical Reviews, November, 2013)