Handbook of Fractional Calculus with Applications Vol 5 Applications in Physics Part B De Gruyter Reference 1st Edition by Vasily E Tarasov ISBN 9783110570892 3110570890

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ISBN 10:  3110570890

ISBN 13: 9783110570892

Author: Vasily E. Tarasov 

Fractional Calculus (FC) originated in 1695, nearly at the same time as conventional calculus. However, FCattracted a limited attention and remained a pure mathematical exercise in spite of the contributions of important mathematicians, physicists, and en-gineers. FC had a rapid development during the last few decades, both in mathematics and applied sciences, being nowadays recognized as an excellent tool for describing complex systems, phenomena involving long range memory effects and nonlocality. A huge number of research papers and books devoted to this subject have been pub-lished, and presently several specialized conferences and workshops are organized each year. The FC popularity in all fields of science is due to its successful application in mathematical models, namely in the form of FC operators and fractional integral and differential equations. Presently, we are witnessing considerable progress both on theoretical aspects and applications of FC in areas such as physics, engineering, biology, medicine, economy, or finance.

The popularity of FC has attracted many researchers from all over the world and there is a demand for works covering all areas of science in a systematic and rigorous form. In fact, the literature devoted to FC and its applications is huge, but readers are confronted with a high heterogeneity and, in some cases, with misleading and inac-curate information. The Handbook of Fractional Calculus with Applications (HFCA) intends to fill that gap and provides the readers with a solid and systematic treatment of the main aspects and applications of FC. Motivated by these ideas, the editors of the volumes involved a team of internationally recognized experts for a joint publish-ing project offering a survey of their own and other important results in their fields of research. As a result of these joint efforts, a modern encyclopedia of FC and its appli-cations, reflecting present day scientific knowledge, is now available with the HFCA. This work is distributed by several distinct volumes, each one developed under the supervision of its editors.

The fourth and fifth volumes of HFCA are devoted to the application of fractional calculus (FC) and fractional differential equations in different areas of physics. These volumes describe the fundamental physical effects and, first of all, those that belong to fractional relaxation-oscillation or diffusion-wave phenomena. The FC allows de-scribe spatial nonlocality and fading memory of power-law type, the openness of phys-ical systems and dissipation, long-range interactions, and other physical phenom-ena. The most well-known physical phenomena and processes, which are described by fractional differential equations, include fractional viscoelasticity, spatial and fre-quency dispersion of power type, nonexponential relaxation, anomalous diffusion, and many others.

The fifth volume of HFCA focuses on the application of FC in various sections of electrodynamics, statistical physics and physical kinetics, quantum mechanics, and quantum field theory. In the 12 chapters, the most important models with nonlocal-ity, memory of the power type, and openness and dissipation are described in such phenomena as the diffusion-wave, fractional and anomalous diffusion, advection-dispersion, nonexponential relaxation, the spatial and frequency dispersion of power-law type in electrodynamics and quantum mechanics, the openness of quantum systems and dissipation.

My special thanks go to the authors of individual chapters that are excellent sur-veys of selected classical and new results in several important fields of FC. The edi-tors believe that the HFCA will represent a valuable and reliable reference work for all scholars and professionals willing to develop research in the challenging and timely scientific area.

Table of contents: 

1 Fractional electromagnetics

2 Fractional electrodynamics with spatial dispersion

3 Fractional-calculus tools applied to study the nonexponential relaxation in dielectrics

4 Fractional diffusion-wave phenomena

5 Fractional diffusion and parametric subordination

6 The fractional advection-dispersion equation for contaminant transport

7 Anomalous diffusion in interstellar medium

8 Fractional kinetics in random/complex media

9 Nonlocal quantum mechanics: fractional calculus approach

10 Fractional quantum fields

11 Fractional quantum mechanics of open quantum systems

12 Fractional quantum mechanics with topological constraint

13 Fractional time quantum mechanics

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Tags: Vasily E Tarasov, Handbook, Fractional Calculus, Applications, Physics, De Gruyter Reference