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Fractional calculus : an introduction for physicists

Author: Richard Herrmann
Publisher: Singapore : World Scientific Publishing Co. Pte. Ltd., [2018] ©2018
Edition/Format:   eBook : Document : English : 3rd editionView all editions and formats
Summary:

The book presents a concise introduction to the basic methods and strategies in fractional calculus which enables the reader to catch up with the state-of-the-art in this field and to participate and  Read more...

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Genre/Form: Electronic books
Additional Physical Format: Print version:
Herrmann, Richard.
Fractional calculus.
[Hackensack], New Jersey : World Scientific, [2018]
(DLC) 2018288923
(OCoLC)1054125617
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Richard Herrmann
ISBN: 9789813274587 9813274581 9789813274594 981327459X
OCLC Number: 1047959929
Description: 1 online resource.
Contents: Intro; Contents; Preface to the Third Edition; Preface to the Second Edition; Preface to the First Edition; Acknowledgments; List of Exercises; 1. Introduction; 2. Functions; 2.1 Gamma function; 2.2 Hypergeometric functions; 2.3 Mittag-Leffler functions; 2.4 Miscellaneous functions; 2.5 Discussion; 2.5.1 Multi-parameter Mittag-Leffler functions; 2.5.2 Fractional probability distributions; 2.5.3 Global Padé approximation of the Mittag-Leffler function; 3. The Fractional Derivative; 3.1 Basics; 3.2 The fractional Leibniz product rule. 3.3 The fractional derivative in terms of finite differences --
The Grünwald-Letnikov derivative; 3.4 Discussion; 3.4.1 Orthogonal polynomials; 3.4.2 Differential representation of the Riemann and Caputo fractional derivative; 4. Friction Forces; 4.1 Classical description; 4.2 Fractional friction; 5. Fractional Calculus; 5.1 The Fourier transform; 5.2 The fractional integral; 5.2.1 The Liouville fractional integral; 5.2.2 The Riemann fractional integral; 5.3 Correlation of fractional integration and differentiation; 5.3.1 The Liouville fractional derivative. 5.3.2 The Riemann fractional derivative; 5.3.3 The Liouville fractional derivative with inverted operator sequence --
The Liouville-Caputo fractional derivative; 5.3.4 The Riemann fractional derivative with inverted operator sequence --
The Caputo fractional derivative; 5.4 Fractional derivative of second order; 5.4.1 The Riesz fractional derivative; 5.4.2 The Feller fractional derivative; 5.5 Fractional derivatives of higher orders --
The Marchaud fractional derivative; 5.6 Erdélyi-Kober operators of fractional integration; 5.7 Geometric interpretation of the fractional integral. 5.8 Low level fractionality; 5.9 Discussion; 5.9.1 Semi-group property of the fractional integral; 6. The Fractional Harmonic Oscillator; 6.1 The fractional harmonic oscillator; 6.2 The harmonic oscillator according to Fourier; 6.3 The harmonic oscillator according to Riemann; 6.4 The harmonic oscillator according to Caputo; 7. Wave Equations and Parity; 7.1 Fractional wave equations; 7.2 Parity and time-reversal; 7.3 Solutions of the free regularized fractional wave equation; 8. Nonlocality and Memory Effects; 8.1 A short history of nonlocal concepts; 8.2 From local to nonlocal operators. 8.3 Memory effects; 9. Fractional Calculus in Multidimensional Space --
2D-Image Processing; 9.1 The generalized fractional derivative; 9.2 Shape recovery --
The local approach; 9.3 Shape recovery --
The nonlocal approach; 10. Fractional Calculus in Multidimensional Space --
3D-Folded Potentials in Cluster Physics --
A Comparison of Yukawa and Coulomb Potentials with Riesz Fractional Integrals; 10.1 Folded potentials in fragmentation theory; 10.2 The Riesz potential as smooth transition between Coulomb and folded Yukawa potential; 10.3 Discussion; 10.3.1 Calculation of a fission yield. 11. Quantum Mechanics.
Responsibility: Richard Herrmann.

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