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Adomian’s decomposition method for solving an intermediate fractional advection-dispersion equation. (English) Zbl 1189.35358
Summary: This paper is concerned with a model that describes the intermediate process between advection and dispersion via fractional derivative in the Caputo sense. Adomian’s decomposition method is used for solving this model. The solution is obtained as an infinite series which always converges to the exact solution.

35R11Fractional partial differential equations
26A33Fractional derivatives and integrals (real functions)
Full Text: DOI
[1] Zheng; Bennett, D.: Applied contaminant transport modeling, (2002)
[2] Todd, K.; Mays, W.: Groundwater hydrology, (2005)
[3] Baeumer, B.; Benson, D. A.; Meerschaert, M. M.: Advection and dispersion in time and space, Physica A 350, 245-262 (2005)
[4] Podlubny, I.; El-Sayed, A. M. A.: On two definitions of fractional calculus, (1996)
[5] Samko, S. G.; Kilvas, A. A.; Maritchev, O. I.: Fractional integrals and derivatives, (1993) · Zbl 0818.26003
[6] Oldham, K. B.; Spanier, J.: The fractional calculus, (1974) · Zbl 0292.26011
[7] Podlubny, I.: Fractional differential equations, (1999) · Zbl 0924.34008
[8] Adomian, G.: Solving frontier problems of physics: the decomposition method, (1994) · Zbl 0802.65122
[9] Adomian, G.: A review of the decomposition method in applied mathematics, J. math. Anal. appl. 135, 501-544 (1988) · Zbl 0671.34053 · doi:10.1016/0022-247X(88)90170-9
[10] El-Sayed, A. M. A.; Gaber, M.: The Adomian decomposition method for solving partial differential equations of fractal order in finite domains, Phys. lett. A 359, 175-182 (2006) · Zbl 1236.35003
[11] El-Sayed, A. M. A.; Gaafar, M.: Fractional calculus and some intermediate physical processes, Appl. math. Comput. 144, 117-126 (2003) · Zbl 1049.35002 · doi:10.1016/S0096-3003(02)00396-X
[12] Magin, R. L.: Anomalous diffusion expressed through fractional order differential operators in the Bloch--torrey equation, J. magn. Reson. 190, 255-270 (2008)