عنوان

Fractional calculus :

شابک

9789814340250

شابک

9814340251

شماره

b548105

عنوان اصلي

Fractional calculus :

نام عام مواد

[Book]

ساير اطلاعات عنواني

an introduction for physicists

نام نخستين پديدآور

Richard Herrmann.

محل نشرو پخش و غیره

Singapore ; Hackensack, N.J.

نام ناشر، پخش کننده و غيره

World Scientific

تاریخ نشرو بخش و غیره

©2011.

نام خاص و کميت اثر

(xii, 261 pages) : illustrations

متن يادداشت

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.

متن يادداشت

Fractional calculus is undergoing and ongoing development. This book presents an introduction to the basics of fractional calculus and guides the reader to the physical interpretation.

موضوع مستند نشده

Engineering & Applied Sciences.

موضوع مستند نشده

Fractional calculus.

موضوع مستند نشده

SCIENCE -- Physics -- Mathematical & Computational.

مستند نام اشخاص تاييد نشده

Richard Herrmann.

مستند نام اشخاص تاييد نشده

Richard Herrmann

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y