General solution of a fractional diffusion–advection equation for solar cosmic-ray transport

• We solve the fractional diffusion–advection equation for solar cosmic-ray transport.
• We give its general solution.
• A numerical analysis of this equation is made.
• We use hypergeometric distributions.

In this effort we exactly solve the fractional diffusion–advection equation for solar cosmic-ray transport and give its general solution in terms of hypergeometric distributions. Numerical analysis of this equation shows that its solutions resemble power-laws.