Abstract
The aim of this paper is to develop a fractional derivative model of energetic particle transport for both uniform and non-uniform large-scale magnetic field by studying the fractional Telegraph equation and the fractional advection–diffusion equation. Analytical solutions of the space–time fractional Telegraph equation and space–time fractional advection–diffusion equation are obtained by use of the Caputo fractional derivative and the Laplace–Fourier technique. The solutions are given in terms of Fox’s H function. As an illustration they are applied to the case of solar energetic particles.
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