Fractional calculus: an introduction for physicists
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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World Scientific
©2011
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| Beschreibung: | Includes bibliographical references (pages 243-256) and index Fractional calculus is undergoing rapidly and ongoing development. We can already recognize, that within its framework new concepts and strategies emerge, which lead to new challenging insights and surprising correlations between different branches of physics. This book is an invitation both to the interested student and the professional researcher. It presents a thorough introduction to the basics of fractional calculus and guides the reader directly to the current state-of-the-art physical interpretation. It is also devoted to the application of fractional calculus on physical problems, in t 1. Introduction -- 2. Functions. 2.1. Gamma function. 2.2. Mittag-Leffler functions. 2.3. Hypergeometric functions. 2.4. Miscellaneous functions -- 3. The fractional derivative. 3.1. Basics. 3.2. The fractional Leibniz product rule. 3.3. Discussion -- 4. Friction forces. 4.1. Classical description. 4.2. Fractional friction -- 5. Fractional calculus. 5.1. The Fourier transform. 5.2. The fractional integral. 5.3. Correlation of fractional integration and differentiation. 5.4. Fractional derivative of second order. 5.5. Fractional derivatives of higher orders. 5.6. Geometric interpretation of the fractional integral. 5.7. Low level fractionality. 5.8. Discussion -- 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. Quantum mechanics. 9.1. Canonical quantization. 9.2. Quantization of the classical Hamilton function and free solutions. 9.3. Temperature dependence of a fission yield and determination of the corresponding fission potential. 9.4. The fractional Schrodinger equation with an infinite well potential. 9.5. Radial solutions of the fractional Schrodinger equation -- 10. Fractional spin : a property of particles described with the fractional Schrodinger equation. 10.1. Spin. 10.2. Fractional spin -- 11. Factorization. 11.1. The Dirac equation. 11.2. The fractional Dirac equation. 11.3. The fractional Pauli equation |
| Beschreibung: | 1 Online-Ressource (xii, 261 pages) |
| ISBN: | 9789814340243 9789814340250 9814340243 9814340251 |
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| 500 | |a Fractional calculus is undergoing rapidly and ongoing development. We can already recognize, that within its framework new concepts and strategies emerge, which lead to new challenging insights and surprising correlations between different branches of physics. This book is an invitation both to the interested student and the professional researcher. It presents a thorough introduction to the basics of fractional calculus and guides the reader directly to the current state-of-the-art physical interpretation. It is also devoted to the application of fractional calculus on physical problems, in t | ||
| 500 | |a 1. Introduction -- 2. Functions. 2.1. Gamma function. 2.2. Mittag-Leffler functions. 2.3. Hypergeometric functions. 2.4. Miscellaneous functions -- 3. The fractional derivative. 3.1. Basics. 3.2. The fractional Leibniz product rule. 3.3. Discussion -- 4. Friction forces. 4.1. Classical description. 4.2. Fractional friction -- 5. Fractional calculus. 5.1. The Fourier transform. 5.2. The fractional integral. 5.3. Correlation of fractional integration and differentiation. 5.4. Fractional derivative of second order. 5.5. Fractional derivatives of higher orders. 5.6. Geometric interpretation of the fractional integral. 5.7. Low level fractionality. 5.8. Discussion -- 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. Quantum mechanics. 9.1. Canonical quantization. 9.2. Quantization of the classical Hamilton function and free solutions. 9.3. Temperature dependence of a fission yield and determination of the corresponding fission potential. 9.4. The fractional Schrodinger equation with an infinite well potential. 9.5. Radial solutions of the fractional Schrodinger equation -- 10. Fractional spin : a property of particles described with the fractional Schrodinger equation. 10.1. Spin. 10.2. Fractional spin -- 11. Factorization. 11.1. The Dirac equation. 11.2. The fractional Dirac equation. 11.3. The fractional Pauli equation | ||
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Datensatz im Suchindex
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| author | Herrmann, Richard |
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| dewey-full | 530.15583 |
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| dewey-ones | 530 - Physics |
| dewey-raw | 530.15583 |
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| spelling | Herrmann, Richard Verfasser aut Fractional calculus an introduction for physicists Richard Herrmann Singapore World Scientific ©2011 1 Online-Ressource (xii, 261 pages) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references (pages 243-256) and index Fractional calculus is undergoing rapidly and ongoing development. We can already recognize, that within its framework new concepts and strategies emerge, which lead to new challenging insights and surprising correlations between different branches of physics. This book is an invitation both to the interested student and the professional researcher. It presents a thorough introduction to the basics of fractional calculus and guides the reader directly to the current state-of-the-art physical interpretation. It is also devoted to the application of fractional calculus on physical problems, in t 1. Introduction -- 2. Functions. 2.1. Gamma function. 2.2. Mittag-Leffler functions. 2.3. Hypergeometric functions. 2.4. Miscellaneous functions -- 3. The fractional derivative. 3.1. Basics. 3.2. The fractional Leibniz product rule. 3.3. Discussion -- 4. Friction forces. 4.1. Classical description. 4.2. Fractional friction -- 5. Fractional calculus. 5.1. The Fourier transform. 5.2. The fractional integral. 5.3. Correlation of fractional integration and differentiation. 5.4. Fractional derivative of second order. 5.5. Fractional derivatives of higher orders. 5.6. Geometric interpretation of the fractional integral. 5.7. Low level fractionality. 5.8. Discussion -- 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. Quantum mechanics. 9.1. Canonical quantization. 9.2. Quantization of the classical Hamilton function and free solutions. 9.3. Temperature dependence of a fission yield and determination of the corresponding fission potential. 9.4. The fractional Schrodinger equation with an infinite well potential. 9.5. Radial solutions of the fractional Schrodinger equation -- 10. Fractional spin : a property of particles described with the fractional Schrodinger equation. 10.1. Spin. 10.2. Fractional spin -- 11. Factorization. 11.1. The Dirac equation. 11.2. The fractional Dirac equation. 11.3. The fractional Pauli equation Calculus Functions Mathematics SCIENCE / Physics / Mathematical & Computational bisacsh Mathematik Fractional calculus Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Gebrochene Analysis (DE-588)4722475-7 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 s Gebrochene Analysis (DE-588)4722475-7 s 1\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=373251 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Herrmann, Richard Fractional calculus an introduction for physicists Calculus Functions Mathematics SCIENCE / Physics / Mathematical & Computational bisacsh Mathematik Fractional calculus Mathematische Physik (DE-588)4037952-8 gnd Gebrochene Analysis (DE-588)4722475-7 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4722475-7 |
| title | Fractional calculus an introduction for physicists |
| title_auth | Fractional calculus an introduction for physicists |
| title_exact_search | Fractional calculus an introduction for physicists |
| title_full | Fractional calculus an introduction for physicists Richard Herrmann |
| title_fullStr | Fractional calculus an introduction for physicists Richard Herrmann |
| title_full_unstemmed | Fractional calculus an introduction for physicists Richard Herrmann |
| title_short | Fractional calculus |
| title_sort | fractional calculus an introduction for physicists |
| title_sub | an introduction for physicists |
| topic | Calculus Functions Mathematics SCIENCE / Physics / Mathematical & Computational bisacsh Mathematik Fractional calculus Mathematische Physik (DE-588)4037952-8 gnd Gebrochene Analysis (DE-588)4722475-7 gnd |
| topic_facet | Calculus Functions Mathematics SCIENCE / Physics / Mathematical & Computational Mathematik Fractional calculus Mathematische Physik Gebrochene Analysis |
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