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Kadem, Abdelouahab; Luchko, Yury; Baleanu, Dumitru

Spectral method for solution of the fractional transport equation. (English) Zbl 1237.82041

Rep. Math. Phys. 66, No. 1, 103-115 (2010).
Summary: The Chebyshev polynomials expansion method is applied to find both an analytical solution of the fractional transport equation in the one-dimensional plane geometry and its numerical approximations. The idea of the method is in reducing of the fractional transport equation to a system of the linear fractional differential equations for the unknown coefficients of the Chebyshev polynomials expansion. The obtained system of equations is then solved by using the operational method for the Caputo fractional derivative.

Cited in 11 Documents

MSC:

82C70 Transport processes in time-dependent statistical mechanics

Keywords:

fractional calculus; fractional transport equation; Chebyshev polynomials
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\textit{A. Kadem} et al., Rep. Math. Phys. 66, No. 1, 103--115 (2010; Zbl 1237.82041)
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