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Fractional calculus : an introduction for physicists / / Richard Herrmann, GigaHedron, Germany
| Fractional calculus : an introduction for physicists / / Richard Herrmann, GigaHedron, Germany |
| Autore | Herrmann Richard |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | Singapore : , : World Scientific, , [2014] |
| Descrizione fisica | 1 online resource (500 p.) |
| Disciplina | 515.8302453 |
| Soggetto topico | Fractional calculus |
| Soggetto genere / forma | Electronic books. |
| ISBN | 981-4551-08-2 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface to the Second Edition; Preface to the First Edition; Acknowledgments; Contents; List of Exercises; 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 The fractional derivative in terms of finite differences - the Grunwald-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 description4.2 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 order5.4.1 The Riesz fractional derivative; 5.4.2 The Feller fractional derivative; 5.5 Fractional derivatives of higher orders - the Marchaud fractional derivative; 5.6 Erdelyi-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 Caputo7. 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 Physics10.1 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; 11.1 Canonical quantization; 11.2 Quantization of the classical Hamilton function and free solutions; 11.3 Temperature dependence of a fission yield and determination of the corresponding fission potential; 11.4 The fractional Schrodinger equation with an infinite well potential 11.5 Radial solutions of the fractional Schrodinger equation |
| Record Nr. | UNINA-9910464695303321 |
Herrmann Richard
|
||
| Singapore : , : World Scientific, , [2014] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fractional calculus : an introduction for physicists
| Fractional calculus : an introduction for physicists |
| Autore | Herrmann Richard |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | New Jersey : , : World Scientific, , [2014] |
| Descrizione fisica | 1 online resource (xix, 479 pages) : illustrations |
| Disciplina | 515.8302453 |
| Collana | Gale eBooks |
| Soggetto topico | Fractional calculus |
| ISBN | 981-4551-08-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface to the Second Edition; Preface to the First Edition; Acknowledgments; Contents; List of Exercises; 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 The fractional derivative in terms of finite differences - the Grunwald-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 description4.2 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 order5.4.1 The Riesz fractional derivative; 5.4.2 The Feller fractional derivative; 5.5 Fractional derivatives of higher orders - the Marchaud fractional derivative; 5.6 Erdelyi-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 Caputo7. 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 Physics10.1 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; 11.1 Canonical quantization; 11.2 Quantization of the classical Hamilton function and free solutions; 11.3 Temperature dependence of a fission yield and determination of the corresponding fission potential; 11.4 The fractional Schrodinger equation with an infinite well potential 11.5 Radial solutions of the fractional Schrodinger equation |
| Record Nr. | UNINA-9910789293503321 |
|
Herrmann Richard
|
||
| New Jersey : , : World Scientific, , [2014] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fractional calculus : an introduction for physicists
| Fractional calculus : an introduction for physicists |
| Autore | Herrmann Richard |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | New Jersey : , : World Scientific, , [2014] |
| Descrizione fisica | 1 online resource (xix, 479 pages) : illustrations |
| Disciplina | 515.8302453 |
| Collana | Gale eBooks |
| Soggetto topico | Fractional calculus |
| ISBN | 981-4551-08-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface to the Second Edition; Preface to the First Edition; Acknowledgments; Contents; List of Exercises; 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 The fractional derivative in terms of finite differences - the Grunwald-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 description4.2 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 order5.4.1 The Riesz fractional derivative; 5.4.2 The Feller fractional derivative; 5.5 Fractional derivatives of higher orders - the Marchaud fractional derivative; 5.6 Erdelyi-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 Caputo7. 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 Physics10.1 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; 11.1 Canonical quantization; 11.2 Quantization of the classical Hamilton function and free solutions; 11.3 Temperature dependence of a fission yield and determination of the corresponding fission potential; 11.4 The fractional Schrodinger equation with an infinite well potential 11.5 Radial solutions of the fractional Schrodinger equation |
| Record Nr. | UNINA-9910807275203321 |
|
Herrmann Richard
|
||
| New Jersey : , : World Scientific, , [2014] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fractional calculus [[electronic resource] ] : an introduction for physicists / / Richard Herrmann
| Fractional calculus [[electronic resource] ] : an introduction for physicists / / Richard Herrmann |
| Autore | Herrmann Richard |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, N.J., : World Scientific, c2011 |
| Descrizione fisica | 1 online resource (274 p.) |
| Disciplina | 515.83 |
| Soggetto topico | Fractional calculus |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-283-14870-6
9786613148704 981-4340-25-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Foreword; Acknowledgments; Contents; 1. Introduction; 2. Functions; 3. The Fractional Derivative; 4. Friction Forces; 5. Fractional Calculus; 6. The Fractional Harmonic Oscillator; 7. Wave Equations and Parity; 8. Nonlocality and Memory Effects; 9. Quantum Mechanics; 10. Fractional Spin: a Property of Particles Described with the Fractional Schr ̈odinger Equation; 11. Factorization; 12. Symmetries; 13. The Fractional Symmetric Rigid Rotor; 14. q-deformed Lie Algebras and Fractional Calculus; 15. Fractional Spectroscopy of Hadrons; 16. Higher Dimensional Fractional Rotation Groups
17. Fractors: Fractional Tensor Calculus18. Fractional Fields; 19. Gauge Invariance in Fractional Field Theories; 20. Outlook; Bibliography; Index |
| Record Nr. | UNINA-9910461293903321 |
|
Herrmann Richard
|
||
| Singapore ; ; Hackensack, N.J., : World Scientific, c2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fractional calculus [[electronic resource] ] : an introduction for physicists / / Richard Herrmann
| Fractional calculus [[electronic resource] ] : an introduction for physicists / / Richard Herrmann |
| Autore | Herrmann Richard |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, N.J., : World Scientific, c2011 |
| Descrizione fisica | 1 online resource (274 p.) |
| Disciplina | 515.83 |
| Soggetto topico | Fractional calculus |
| ISBN |
1-283-14870-6
9786613148704 981-4340-25-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Foreword; Acknowledgments; Contents; 1. Introduction; 2. Functions; 3. The Fractional Derivative; 4. Friction Forces; 5. Fractional Calculus; 6. The Fractional Harmonic Oscillator; 7. Wave Equations and Parity; 8. Nonlocality and Memory Effects; 9. Quantum Mechanics; 10. Fractional Spin: a Property of Particles Described with the Fractional Schr ̈odinger Equation; 11. Factorization; 12. Symmetries; 13. The Fractional Symmetric Rigid Rotor; 14. q-deformed Lie Algebras and Fractional Calculus; 15. Fractional Spectroscopy of Hadrons; 16. Higher Dimensional Fractional Rotation Groups
17. Fractors: Fractional Tensor Calculus18. Fractional Fields; 19. Gauge Invariance in Fractional Field Theories; 20. Outlook; Bibliography; Index |
| Record Nr. | UNINA-9910789409903321 |
|
Herrmann Richard
|
||
| Singapore ; ; Hackensack, N.J., : World Scientific, c2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fractional calculus [[electronic resource] ] : an introduction for physicists / / Richard Herrmann
| Fractional calculus [[electronic resource] ] : an introduction for physicists / / Richard Herrmann |
| Autore | Herrmann Richard |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, N.J., : World Scientific, c2011 |
| Descrizione fisica | 1 online resource (274 p.) |
| Disciplina | 515.83 |
| Soggetto topico | Fractional calculus |
| ISBN |
1-283-14870-6
9786613148704 981-4340-25-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Foreword; Acknowledgments; Contents; 1. Introduction; 2. Functions; 3. The Fractional Derivative; 4. Friction Forces; 5. Fractional Calculus; 6. The Fractional Harmonic Oscillator; 7. Wave Equations and Parity; 8. Nonlocality and Memory Effects; 9. Quantum Mechanics; 10. Fractional Spin: a Property of Particles Described with the Fractional Schr ̈odinger Equation; 11. Factorization; 12. Symmetries; 13. The Fractional Symmetric Rigid Rotor; 14. q-deformed Lie Algebras and Fractional Calculus; 15. Fractional Spectroscopy of Hadrons; 16. Higher Dimensional Fractional Rotation Groups
17. Fractors: Fractional Tensor Calculus18. Fractional Fields; 19. Gauge Invariance in Fractional Field Theories; 20. Outlook; Bibliography; Index |
| Record Nr. | UNINA-9910809011103321 |
|
Herrmann Richard
|
||
| Singapore ; ; Hackensack, N.J., : World Scientific, c2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||