An approximate solution of nonlinear fractional reaction–diffusion equation

The article presents a mathematical model of nonlinear reaction diffusion equation with fractional time derivative α (0 < α ⩽ 1) in the form of a rapidly convergent series with easily computable components. Fractional reaction diffusion equation is used for modeling of merging travel solutions in nonlinear system for popular dynamics. The fractional derivatives are described in the Caputo sense. The anomalous behaviors of the nonlinear problems in the form of sub- and super-diffusion due to the presence of reaction term are shown graphically for different particular cases.