LEADER 05232nam 2200625 450 001 9910464695303321 005 20200520144314.0 010 $a981-4551-08-2 035 $a(CKB)3710000000092941 035 $a(EBL)1647252 035 $a(SSID)ssj0001180000 035 $a(PQKBManifestationID)12512748 035 $a(PQKBTitleCode)TC0001180000 035 $a(PQKBWorkID)11187236 035 $a(PQKB)10668035 035 $a(MiAaPQ)EBC1647252 035 $a(WSP)00005697 035 $a(Au-PeEL)EBL1647252 035 $a(CaPaEBR)ebr10845321 035 $a(CaONFJC)MIL580915 035 $a(OCoLC)873140206 035 $a(EXLCZ)993710000000092941 100 $a20140320h20142014 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFractional calculus $ean introduction for physicists /$fRichard Herrmann, GigaHedron, Germany 205 $aSecond edition. 210 1$aSingapore :$cWorld Scientific,$d[2014] 210 4$dİ2014 215 $a1 online resource (500 p.) 300 $aDescription based upon print version of record. 311 $a981-4551-07-4 320 $aIncludes bibliographical references (p. 439-472) and index. 327 $aPreface 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 327 $a4.1 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 327 $a5.4 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 327 $a6.4 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 327 $a10. 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 327 $a11.5 Radial solutions of the fractional Schrodinger equation 330 $aThe 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, extende 606 $aFractional calculus 608 $aElectronic books. 615 0$aFractional calculus. 676 $a515.8302453 700 $aHerrmann$b Richard$0478610 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910464695303321 996 $aFractional calculus$9263675 997 $aUNINA