STUDY AND ANALYSIS OF SPATIAL-TIME NONLINEAR FRACTIONAL-ORDER REACTION-ADVECTION-DIFFUSION EQUATION

In the present article, the Legendre collocation method is used to solve the fractional-order advection-diffusion equation having a nonlinear type source/sink term with initial and boundary conditions. The solution profiles of the normalized solute concentration for both reaction-advection-diffusion and reaction-diffusion systems are presented through graphs for different particular cases. The salient features of the article are the pictorial presentations of the effects of fractional-order spatial and time derivatives as well as the advection term on the solution profile. An initiative has been taken to compare the numerical solution of our proposed method with the existing analytical solution through error analysis, which is exhibited through figures and a table.