  This work studies exact solvability of a class of fractional
reaction-diffusion equation with the Riemann-Liouville fractional derivatives
on the half-line in terms of the similarity solutions. We derived the
conditions for the equation to possess scaling symmetry even with the
fractional derivatives. Relations among the scaling exponents are determined,
and the appropriate similarity variable introduced. With the similarity
variable we reduced the stochastic partial differential equation to a
fractional ordinary differential equation. Exactly solvable systems are then
identified by matching the resulted ordinary differential equation with the
known exactly solvable fractional ones. Several examples involving the
three-parameter Mittag-Leffler function (Kilbas-Saigo function) are presented.
The models discussed here turn out to correspond to superdiffusive systems.
