Similarity solutions for a class of Fractional Reaction-Diffusion equation
arXiv:2004.06198 · doi:10.1016/j.cjph.2020.10.022
Abstract
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.
15 pages, 4 figures
References in corpus (17)
- Fractional Schrodinger equation
- Fractional Quantum Mechanics
- The fundamental solution of the space-time fractional diffusion equation
- Anomalous diffusion in the presence of external forces: exact time-dependent solutions and entropy
- Time fractional Schrodinger equation
- A practical guide to Prabhakar fractional calculus
- Lévy flights in random environments
- Fractional Reaction-Diffusion Equation
- Fractional Fokker-Planck Equations for Subdiffusion with Space-and-Time-Dependent Forces
- Nonlinear equation for anomalous diffusion: unified power-law and stretched exponential exact solution
- Nonlinear anomalous diffusion equation and fractal dimension: Exact generalized gaussian solution
- Similarity solutions of Fokker-Planck equation with time-dependent coefficients
- Similarity solutions of Fokker-Planck equation with moving boundaries
- Convection-Diffusion-Reaction equation with similarity solutions
- Similarity solutions of Reaction-Diffusion equation with space- and time-dependent diffusion and reaction terms
- Symmetry analysis for time-fractional convection-diffusion equation
- Similarity solutions of Fokker-Planck equation with time-dependent coefficients and fixed/moving boundaries