Abstract
The fundamental solution to the Cauchy problem for the space-time-fractional advection diffusion equation with the Caputo time-fractional derivative and Riesz fractional Laplace operator is considered in a case of two spatial variables. The solution is obtained using the Laplace integral transform with respect to time t and the double Fourier transform with respect to space variables x and y. Several particular cases of the solution are analyzed in details. Numerical results are illustrated graphically.
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Povstenko, Y. (2015). Space-Time-Fractional Advection Diffusion Equation in a Plane. In: Latawiec, K., Łukaniszyn, M., Stanisławski, R. (eds) Advances in Modelling and Control of Non-integer-Order Systems. Lecture Notes in Electrical Engineering, vol 320. Springer, Cham. https://doi.org/10.1007/978-3-319-09900-2_26
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DOI: https://doi.org/10.1007/978-3-319-09900-2_26
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-09899-9
Online ISBN: 978-3-319-09900-2
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