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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.
We consider similarity solutions of the generalized convection-diffusion-reaction equation with both space- and time-dependent convection, diffusion and reaction terms. By introducing the similarity variable, the reaction-diffusion equation is reduce
The stochastic solution with Gaussian stationary increments is establihsed for the symmetric space-time fractional diffusion equation when $0 < beta < alpha le 2$, where $0 < beta le 1$ and $0 < alpha le 2$ are the fractional derivation orders in tim
Levy walks define a fundamental concept in random walk theory which allows one to model diffusive spreading that is faster than Brownian motion. They have many applications across different disciplines. However, so far the derivation of a diffusion e
This paper deals with the investigation of the computational solutions of an unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the generalized fra
We consider solvability of the generalized reaction-diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction-diffusion equation is redu