A physical interpretation for the fractional derivative in Levy diffusion

Applied Mathematics Letters

Volumn 15, Issue 7, 2002, Pages 907-911

  Molz III, F J ^a   Fix III, G J ^a   Lu, Silong ^a  

^a CLEMSON UNIVERSITY   (United States)

Author keywords

Fractional derivatives; Levy motion; Solute flux; Superposition

Indexed keywords

EID: 31244438428     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-9659(02)00062-9     Document Type: Article

References (10)

1. M.M. Meerschaert, D.A. Benson and B. Baumer, Multidimensional advection and fractional dispersion, Phys. Rev. E 59, 5026-5028, (1999).
2. I. Podlubny, Fractional Differential Equations, Academic Press, New York, (1999).
3. K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley and Sons, New York, (1993).
4. S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional Integrals and Derivatives, Gordon and Breach, Amsterdam, (1993).
5. A. Compte, Stochastic foundations of fractional dynamics, Phys. Rev. E 53, 4191-4193, (1996).
6. A. Compte, Continuous time random walks in moving fluids, Phys. Rev. E 55, 6821-6831, (1997).
7. A.S. Chavez, A fractional diffusion equation to describe Levy flights, Phys. Lett. A 239, 13-16, (1998).
8. R. Metzler and T.F. Nonnenmacher, Fractional diffusion, waiting-time distributions, and Cattaneo-type equations, Phys. Rev. E 57, 6409-6414, (1998).
9. D.A. Benson, S.W. Wheatcraft and M.M. Meerschaert, Application of a fractional advection-dispersion equation, Water Resour. Res. 36, 1403-1412, (2000).
10. D.A. Benson, S.W. Wheatcraft and M.M. Meerschaert, The fractional order governing equation of Levy motion, Water Resour. Res. 36, 1413-1423, (2000).