Space-Time-Fractional Advection Diffusion Equation in a Plane

  • Yuriy Povstenko
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 320)


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.


Fractional calculus advection diffusion equation Caputo derivative Riesz operator 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute of Mathematics and Computer ScienceJan Dlugosz University in CzȩstochowaCzȩstochowaPoland

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