Analytical solution of the space-time fractional hyperdiffusion equation

The so-called fractional hyperdiffusion equation is presented to develop a fractional derivative model of the transport of energetic particles. The fractional hyperdiffusion equation is defined in terms of Caputo and Riesz fractional derivatives for time and space, respectively. The solution is obtained by using the Laplace-Fourier transforms and given in terms of the M-Wright and Fox's H functions. Profiles of particle densities are illustrated for different values of space-fractional order.