Fundamental Solutions to Time-Fractional Advection Diffusion Equation in a Case of Two Space Variables

The fundamental solutions to time-fractional advection diffusion equation in a plane and a half-plane are obtained using the Laplace integral transform with respect to time t and the Fourier transforms with respect to the space coordinates x and y. The Cauchy, source, and Dirichlet problems are investigated. The solutions are expressed in terms of integrals of Bessel functions combined with Mittag-Leffler functions. Numerical results are illustrated graphically.