Geodesic
Integral Transforms Method to Solve a Time-Space Fractional Diffusion Equation
Fractional calculus and applied analysis, Tome 13 (2010) no. 1, pp. 57-68.

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The method of integral transforms based on using a fractional generalization of the Fourier transform and the classical Laplace transform is applied for solving Cauchy-type problem for the time-space fractional diffusion equation expressed in terms of the Caputo time-fractional derivative and a generalized Riemann-Liouville space-fractional derivative.
Keywords: Caputo Fractional Derivative, Fractional Diffusion Equation, Laplace Transform, Fractional Fourier Transform 
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Nikolova, Yanka; Boyadjiev, Lyubomir. Integral Transforms Method to Solve a Time-Space Fractional Diffusion Equation. Fractional calculus and applied analysis, Tome 13 (2010) no. 1, pp. 57-68. http://geodesic.mathdoc.fr/item/FCAA_2010_13_1_a4/