Geodesic
Numerical Approximation of a Fractional-In-Space Diffusion Equation (II) – with Nonhomogeneous Boundary Conditions
Fractional calculus and applied analysis, Tome 9 (2006) no. 4, pp. 333-349.

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In this paper, a space fractional diffusion equation (SFDE) with nonhomogeneous boundary conditions on a bounded domain is considered. A new matrix transfer technique (MTT) for solving the SFDE is proposed. The method is based on a matrix representation of the fractional-in-space operator and the novelty of this approach is that a standard discretisation of the operator leads to a system of linear ODEs with the matrix raised to the same fractional power. Analytic solutions of the SFDE are derived. Finally, some numerical results are given to demonstrate that the MTT is a computationally efficient and accurate method for solving SFDE.
Keywords: Fractional Diffusion, Anomalous Diffusion, Non-Homogeneous Boundary Conditions, Numerical Approximation, 26A33, 35S15 
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     author = {Ilic, M. and Liu, F. and Turner, I. and Anh, V.},
     title = {Numerical {Approximation} of a {Fractional-In-Space} {Diffusion} {Equation} {(II)} {\textendash} with {Nonhomogeneous} {Boundary} {Conditions}},
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Ilic, M.; Liu, F.; Turner, I.; Anh, V. Numerical Approximation of a Fractional-In-Space Diffusion Equation (II) – with Nonhomogeneous Boundary Conditions. Fractional calculus and applied analysis, Tome 9 (2006) no. 4, pp. 333-349. http://geodesic.mathdoc.fr/item/FCAA_2006_9_4_a1/