Fractional calculus. An introduction for physicists. 2nd extended ed. (English) Zbl 1293.26001

Herrmann, Richard

Hackensack, NJ: World Scientific (ISBN 978-981-4551-07-6/hbk; 978-981-4551-09-0/ebook). xix, 479 p. (2014).

The book is devoted to the application of fractional calculus to physical problems. The fractional concept is applied to subjects in classical mechanics, group theory, quantum mechanics, nuclear physics, hadron spectroscopy up to quantum field theory. The book realizes the interesting property of fractional order (FO) derivative, namely memory and non-locality, which possibly makes FO suitable to investigate quantum mechanics and related systems. It is also suitable to study complex adaptive systems, e.g. biological, social and economic systems. A relation between \(q\)-deformed algebras and strong interactions has not been mentioned. The book has the property that derived results are directly compared with experimental findings. As a consequence, the reader is guided and encouraged to apply the fractional calculus approach in her/his research area. It is highly expected that the viewpoint of fractional calculus will lead to new insights and interesting results. A valuable addition to the second edition is the exercises-solutions section. Further additions include image processing, folded potentials in cluster physics, infrared spectroscopy and fractional calculus with variable order. The significant change in size between the two editions within a short period indicates the importance of fractional calculus. The reviewer strongly recommends this book for beginners as well as specialists in the fields of physics, mathematics and complex adaptive systems.
For the first edition see [Zbl 1232.26006].

Reviewer: E. Ahmed (Mansoura)

MSC:

26-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions
26A33	Fractional derivatives and integrals
70-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of particles and systems
74-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids
81-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory

Keywords:

fractional calculus; quantum systems

Citations:

Zbl 1232.26006