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Fractional radiative transfer equation within Chebyshev spectral approach. (English) Zbl 1189.35359
Summary: We report the convergence of the Chebyshev polynomials combined with the $SN$ method for the steady state transport equation using the fractional derivative. The procedure is based on the expansion of the angular flux in a truncated series of orthogonal polynomials that results in the transformation of the multidimensional problem into a system of fractional differential equations. The convergence of this approach is studied in the context of the multidimensional discrete-ordinates equations.
##### MSC:
 35R11 Fractional partial differential equations 26A33 Fractional derivatives and integrals (real functions) 76R50 Diffusion (fluid mechanics)