Fractional wave equation and damped waves

Journal of Mathematical Physics

Volumn 54, Issue 3, 2013, Pages

  Luchko, Yuri ^a  

^a BEUTH UNIVERSITY OF APPLIED SCIENCES   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84875877772     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4794076     Document Type: Article

References (34)

1. Uchaikin V.V. Fractional Derivatives for Physicists and Engineers: Vol. I Background and Theory, Vol. II Applications 2013, (Springer, ).
2. Herrmann R. Fractional Calculus: An Introduction for Physicists 2011, (World Scientific, ).
3. Freed A. Diethelm K. Luchko Y. Fractional-Order Viscoelasticity (FOV): Constitutive Development Using the Fractional Calculus 2002, and (NASA's Glenn Research Center, ).
4. Hilfer R. Applications of Fractional Calculus in Physics 2000, (World Scientific, ).
5. Klages R. Radons G. Sokolov I.M. Anomalous Transport: Foundations and Applications 2008, and (Wiley-VCH, ).
6. Luchko Y. Punzi A. Modeling anomalous heat transport in geothermal reservoirs via fractional diffusion equations. Int. J. Geomath. 2011, 1:257-276. 10.1007/s13137-010-0012-8, and ",".
7. Luchko Y. Anomalous diffusion models and their analysis. Forum Berl. Math. Ges. 2011, 19:53-85. ",".
8. Magin R.L. Magin R.L. Magin R.L. Fractional calculus in bioengineering: Parts 1, 2, and 3. Crit. Rev. Biomed. Eng. 2004, 32:195-377. 10.1615/CritRevBiomedEng.v32.10, 10.1615/CritRevBiomedEng.v32.i2.10, 10.1615/CritRevBiomedEng.v32.i34.10;, ;.
9. Mainardi F. Fractional relaxation-oscillation and fractional diffusion-wave phenomena. Chaos, Solitons Fractals 1996, 7:1461-1477. 10.1016/0960-0779(95)00125-5, ",".
10. Mainardi F. Fractional Calculus and Waves in Linear Viscoelasticity 2010, (Imperial College, ).
11. Metzler R. Klafter J. The restaurant at the end of the random walk: Recent developments in the description of anomalous transport by fractional dynamics. J. Phys. A 2004, 37:R161-R208. 10.1088/0305-4470/37/31/R01, and ",".
12. Fujita Y. Integrodifferential equation which interpolates the heat equation and the wave equation. Osaka J. Math. 1990, 27:309-321. ",".
13. Luchko Y. Mainardi F. Povstenko Y. Propagation speed of the maximum of the fundamental solution to the fractional diffusion-wave equation. Computers & Mathematics with Applications 10.1016/j.camwa.2013.01.005, and "," (in press);e-print arXiv:1201.5313v1 [math-ph].
14. Gorenflo R. Iskenderov A. Luchko Y. Mapping between solutions of fractional diffusion-wave equations. Fractional Calculus Appl. Anal. 2000, 3:75-86. and ",".
15. Mainardi F. Luchko Y. Pagnini G. The fundamental solution of the space-time fractional diffusion equation. Fractional Calculus Appl. Anal. 2001, 4:153-192. and ",".
16. Metzler R. Nonnenmacher T.F. Space- and time-fractional diffusion and wave equations, fractional Fokker-Planck equations, and physical motivation. Chem. Phys. 2002, 284:67-90. 10.1016/S0301-0104(02)00537-2, and ",".
17. Gorenflo R. Mainardi F. Random walk models approximating symmetric space-fractional diffusion processes. Problems in Mathematical Physics 2001, 120-145. J. Elschner, I. Gohberg, B. Silbermann, and "," in edited by and (Birkhäuser, Verlag, ), pp.
18. Saichev A. Zaslavsky G. Fractional kinetic equations: Solutions and applications. Chaos 1997, 7:753-764. 10.1063/1.166272, and ",".
19. Samko S.G. Kilbas A.A. Marichev O.I. Fractional Integrals and Derivatives: Theory and Applications 1993, and (Gordon and Breach, ).
20. Feller W. On a generalization of Marcel Riesz' potentials and the semi-groups generated by them. Meddelanden Lunds Universitets Matematiska Seminarium (Comm. Sém. Mathém. Université de Lund), Tome suppl. dédié à M. Riesz 1952, 73-81. "," pp.
21. Gorenflo R. Mainardi F. Random walk models for space-fractional diffusion processes. Fractional Calculus Appl. Anal. 1998, 1:167-191. and ",".
22. Luchko Y. Operational method in fractional calculus. Fractional Calculus Appl. Anal. 1999, 2:463-489. ",".
23. Podlubny I. Fractional Differential Equations 1999, (Academic, ).
24. Marichev O.I. Handbook of Integral Transforms of Higher Transcendental Functions, Theory and Algorithmic Tables 1983, (Ellis Horwood, ).
25. Yakubovich S. Luchko Y. The Hypergeometric Approach to Integral Transforms and Convolutions 1994, and (Kluwer Academic, ).
26. Schneider W.R. Wyss W. Fractional diffusion and wave equations. J. Math. Phys. 1989, 30:134-144. 10.1063/1.528578, and ",".
27. Gurwich I. On the pulse velocity in absorbing and nonlinear media and parallels with the quantum mechanics. Prog. Electromagn. Res. 2001, 33:69-96. 10.2528/PIER00071802, ",".
28. Prudnikov A.P. Brychkov Y. Marichev O.I. Integrals and Series, Vol. 1: Elementary Functions 1986, and (Gordon and Breach, ).
29. Carcione J.M. Gei D. Treitel S. The velocity of energy through a dissipative medium. Geophysics 2010, 75:T37-T47. 10.1190/1.3346064, and ",".
30. Bloch S.C. Eighth velocity of light. Am. J. Phys. 1977, 45:538-549. 10.1119/1.10953, ",".
31. van Groesen E. Mainardi F. Energy propagation in dissipative systems, Part I: Centrovelocity for linear systems. Wave Motion 1989, 11:201-209. 10.1016/0165-2125(89)90001-2, and ",".
32. van Groesen E. Mainardi F. Balance laws and centrovelocity in dissipative systems. J. Math. Phys. 1990, 31:2136-2140. 10.1063/1.528666, and ",".
33. Mainardi F. Energy propagation for dispersive waves in dissipative media. Radiofisika [Radiophys. Quantum Electron.] 1993, 36:650-664. ",".
34. Smith R.L. The velocities of light. Am. J. Phys. 1970, 38:978-984. 10.1119/1.1976551, ",".