Study on the Density-Independent Fractional Diffusion-Reaction Equation with the Beta Derivative

In this paper, the density-independent fractional diffusion-reaction (FDR) equation involving quadratic nonlinearity is investigated. The fractional derivative is illustrated in the beta derivative sense. We firstly propose Bernoulli [see formula in PDF]-expansion method to study nonlinear fractional differential equations (NFDEs). Subsequently, closed form solutions of the density-independent FDR equation are acquired successfully. In order to better understand the dynamic behaviors of these solutions, 3D, contour map and line plots are given by the computer simulation. The results show that the proposed method is a reliable and efficient approach.