General solution of a fractional Parker diffusion-convection equation describing the superdiffusive transport of energetic particles
Institut für Theoretische Physik IV, Ruhr-Universität Bochum, Universitätsstrasse 150, D-44780, Bochum, Germany
2 Theoretical Physics Research Group, Mansoura University, 35516, Mansoura, Egypt
* e-mail: Ashraf.Attia@ruhr-uni-bochum.de
Accepted: 2 May 2018
Published online: 1 June 2018
Anomalous diffusion models of energetic particles in space plasmas are developed by introducing the fractional Parker diffusion-convection equation. Analytical solution of the space-time fractional equation is obtained by use of the Caputo and Riesz-Feller fractional derivatives with the Laplace-Fourier transforms. The solution is given in terms of the Fox H-function. Profiles of particle densities are illustrated for different values of the space fractional order and the so-called skewness parameter.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2018