Fundamental solutions to time-fractional advection diffusion equation in a case of two space variables (Q1718982)

Summary: 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.