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An implicit approximation for the Caputo fractional reaction-dispersion equation. (Chinese. English summary) Zbl 1164.65528
Summary: Fractional differential equations can simulate many phenomena contrasting with integer differential equations in lots of applied science. In this paper, a time-fractional reaction-dispersion equation is considered in which the first order derivative is replaced by a Caputo fractional derivative, and an implicit difference scheme is given. Stability and convergence are proved by using the energy method. A numerical example demonstrates that the difference method is effective.

MSC:
65R20Integral equations (numerical methods)
65M06Finite difference methods (IVP of PDE)
65M12Stability and convergence of numerical methods (IVP of PDE)
35K57Reaction-diffusion equations
45K05Integro-partial differential equations
45G10Nonsingular nonlinear integral equations
26A33Fractional derivatives and integrals (real functions)