Fractional calculus is a collection of relatively little-known mathematical results concerning generalizations of differentiation and integration to noninteger orders. While these results have been accumulated over centuries in various branches of mathematics, they have until recently found little appreciation or application in physics and other mathematically oriented sciences. This situation is beginning to change, and there are now a growing number of research areas in physics which employ fractional calculus. This volume provides an introduction to fractional calculus for physicists, and collects easily accessible review articles surveying those areas of physics in which applications of fractional calculus have recently become prominent
Author(s): Rudolf Hilfer
Publisher: World Scientific
Year: 2000
Language: English
Pages: vii, 463 p. : ill
City: Singapore ; River Edge, NJ
Tags: Физика;Матметоды и моделирование в физике;
Content: Chapter I. An Introduction to Fractional Calculus Chapter II. Fractional Time Evolution Chapter III. Fractional Powers of Infinitesimal Generators of Semigroups Chapter IV. Fractional Differences, Derivatives and Fractal Time Series Chapter V. Fractional Kinetics of Hamiltonian Chaotic Systems Chapter VI. Polymer Science Applications of Path-Integration, Integral Equations, and Fractional Calculus Chapter VII. Applications to Problems in Polymer Physics and Rheology Chapter VIII. Applications of Fractional Calculus Techniques to Problems in Biophysics Chapter IX. Fractional Calculus and Regular Variation in Thermodynamics.
Abstract: Nine independent treatments that have been only lightly edited to retain the diverse styles and levels of formalization in the different areas of application. A unifying theme is that fractional derivatives arise as the infinitesimal generators of a class of translation- invariant convolution semigroups, which appear universally as attractors for coarse graining procedures or scale change, and are parametrized by a number in the unit interval corresponding to the order of the fractional derivative. After an introduction to fractional calculus, the topics include fractional time evolution, the fractional kinetics of Hamiltonian chaotic systems, and applications to problems in polymer physics and rheology
