Fractional Calculus: An Introduction for Physicists

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World Scientific, 12.02.2001 - 636 Seiten
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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 contribute in the development of this exciting research area.

This book is devoted to the application of fractional calculus on physical problems. The fractional concept is applied to subjects in classical mechanics, image processing, folded potentials in cluster physics, infrared spectroscopy, group theory, quantum mechanics, nuclear physics, hadron spectroscopy up to quantum field theory and will surprise the reader with new intriguing insights.

This new, extended edition includes additional chapters about numerical solution of the fractional Schrödinger equation, self-similarity and the geometric interpretation of non-isotropic fractional differential operators. Motivated by the positive response, new exercises with elaborated solutions are added, which significantly support a deeper understanding of the general aspects of the theory.

Besides students as well as researchers in this field, this book will also be useful as a supporting medium for teachers teaching courses devoted to this subject.

 

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Inhalt

1 Introduction
1
2 Functions
7
3 The Fractional Derivative
37
4 Friction Forces
55
5 Fractional Calculus
65
6 The Fractional Harmonic Oscillator
91
7 Wave Equations and Parity
99
8 Nonlocality and Memory Effects
109
18 qDeformed Lie Algebras and Fractional Calculus
277
19 Infrared Spectroscopy of Diatomic Molecules
291
20 Fractional Spectroscopy of Hadrons
311
21 Magic Numbers in Atomic Nuclei
337
22 Magic Numbers in Metal Clusters
373
23 Towards a Geometric Interpretation of Generalized Fractional Integrals
387
24 Fractors Fractional Tensor Calculus
417
25 Fractional Fields
421

9 Fractional Calculus in Multidimensional Space 2DImage Processing
129
10 Fractional Calculus in Multidimensional Space 3DFolded Potentials in Cluster Physics A Comparison of Yukawa and Coulomb Potentials with Ri...
143
11 Quantum Mechanics
163
12 The Fractional Schrödinger Equation with Infinite Well Potential Numerical Results Using the Riesz Derivative
189
13 Uniqueness of a Fractional Derivative The Riesz and Regularized Liouville Derivative as Examples
201
14 Fractional Spin A Property of Particles Described with the Fractional Schrödinger Equation
221
15 Factorization
227
16 Symmetries
245
17 The Fractional Symmetric Rigid Rotor
255
26 Gauge Invariance in Fractional Field Theories
433
The One Dimensional Case
443
28 On the Origin of Space
491
29 Outlook
507
Appendix A Solutions to Exercises
509
Bibliography
557
Index
603
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