Fractional calculus an introduction for physicists
The book presents a concise introduction to the basic methods and strategies in fractional calculus and enables the reader to catch up with the state of the art in this field as well as to participate and contribute in the development of this exciting research area. The contents are devoted to the a...
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| Main Author | |
|---|---|
| Format | eBook Book |
| Language | English |
| Published |
Hackensack, NJ
World Scientific Publishing Co. Pte. Ltd
2014
World Scientific WORLD SCIENTIFIC WSPC |
| Edition | 2nd ed. |
| Subjects | |
| Online Access | Get full text |
| ISBN | 9814551082 9789814551076 9814551074 9789814551083 |
| DOI | 10.1142/8934 |
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| Abstract | The book presents a concise introduction to the basic methods and strategies in fractional calculus and enables the reader to catch up with the state of the art in this field as well as to participate and contribute in the development of this exciting research area. The contents are 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 and quantum field theory and it will surprise the reader with new intriguing insights. |
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| AbstractList | The book presents a concise introduction to the basic methods and strategies in fractional calculus and enables the reader to catch up with the state of the art in this field as well as to participate and contribute in the development of this exciting research area.
The contents are 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 and quantum field theory and it will surprise the reader with new intriguing insights.
This new, extended edition now also covers additional chapters about image processing, folded potentials in cluster physics, infrared spectroscopy and local aspects of fractional calculus. A new feature is exercises with elaborated solutions, which significantly supports a deeper understanding of general aspects of the theory. As a result, this book should also be useful as a supporting medium for teachers and courses devoted to this subject. The book presents a concise introduction to the basic methods and strategies in fractional calculus and enables the reader to catch up with the state of the art in this field as well as to participate and contribute in the development of this exciting research area.The contents are 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 and quantum field theory and it will surprise the reader with new intriguing insights.This new, extended edition now also covers additional chapters about image processing, folded potentials in cluster physics, infrared spectroscopy and local aspects of fractional calculus. A new feature is exercises with elaborated solutions, which significantly supports a deeper understanding of general aspects of the theory. As a result, this book should also be useful as a supporting medium for teachers and courses devoted to this subject. The book presents a concise introduction to the basic methods and strategies in fractional calculus and enables the reader to catch up with the state of the art in this field as well as to participate and contribute in the development of this exciting research area. The contents are 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 and quantum field theory and it will surprise the reader with new intriguing insights. |
| Author | Herrmann, Richard |
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| DOI | 10.1142/8934 |
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| Discipline | Applied Sciences Mathematics Physics |
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| Edition | 2nd ed. 2 2nd edition. |
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| Keywords | Fractional Calculus Non-Local Field Theories Long-Memory Kernels Mathematical Physics Fractional Quantum Mechanics |
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| Notes | Includes bibliographical references and index |
| PageCount | 500 |
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| PublicationDate | 2014. c2014 20140300 2014-01-03 |
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| PublicationDecade | 2010 |
| PublicationPlace | Hackensack, NJ |
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| Publisher | World Scientific Publishing Co. Pte. Ltd World Scientific WORLD SCIENTIFIC WSPC |
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| Snippet | The book presents a concise introduction to the basic methods and strategies in fractional calculus and enables the reader to catch up with the state of the... |
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| SubjectTerms | Fractional calculus |
| SubjectTermsDisplay | Fractional calculus |
| Subtitle | an introduction for physicists |
| TableOfContents | Fractional calculus : an introduction for physicists -- Preface to the Second Edition -- Preface to the First Edition -- Acknowledgments -- Contents -- Chapter 1: Introduction -- Chapter 2: Functions -- Chapter 3: The Fractional Derivative -- Chapter 4: Friction Forces -- Chapter 5: Fractional Calculus -- Chapter 6: The Fractional Harmonic Oscillator -- Chapter 7: Wave Equations and Parity -- Chapter 8: Nonlocality and Memory Effects -- Chapter 9: Fractional Calculus in Multidimensional Space 2DImage Processing -- Chapter 10: Fractional Calculus in Multidimensional Space 3D-Folded Potentials in Cluster Physics - a Comparison of Yukawa and Coulomb Potentials with Riesz Fractional Integrals -- Chapter 11: Quantum Mechanics -- Chapter 12: The Fractional Schrจodinger Equation with the Infinite Well Potential Numerical Results using the Riesz Derivative -- Chapter 13: Uniqueness of a Fractional Derivative the Riesz and Regularized Liouville Derivative as Examples -- Chapter 14: Fractional Spin A Property of Particles Described with the Fractional Schrจodinger Equation -- Chapter 15: Factorization -- Chapter 16: Symmetries -- Chapter 17: The Fractional Symmetric Rigid Rotor -- Chapter 18: q-deformed Lie Algebras and Fractional Calculus -- Chapter 19: Infrared Spectroscopy of Diatomic Molecules -- Chapter 20: Fractional Spectroscopy of Hadrons -- Chapter 21: Magic Numbers in Atomic Nuclei -- Chapter 22: Magic Numbers in Metal Clusters -- Chapter 23: Fractors Fractional Tensor Calculus -- Chapter 24: Fractional Fields -- Chapter 25: Gauge Invariance in Fractional Field Theories -- Chapter 26: On the Origin of Space -- Chapter 27: Outlook -- Appendix A: Solutions to Exercises -- Bibliography -- Index. |
| Title | Fractional calculus |
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