Study of two-dimensional nonlinear coupled time-space fractional order reaction advection diffusion equations using shifted Legendre-Gauss-Lobatto collocation method

In this article, the nonlinear coupled two-dimensional space-time fractional order reaction-advection–diffusion equations (2D-STFRADEs) with initial and boundary conditions is solved by using Shifted Legendre-Gauss-Lobatto Collocation method (SLGLCM) with fractional derivative defined in Caputo sense. The SLGLC scheme is used to discretize the coupled nonlinear 2D-STFRADEs into the shifted Legendre polynomial roots to convert it to a system of algebraic equations. The efficiency and efficacy of the scheme are confirmed through error analysis while applying the scheme on two existing problems having exact solutions. The impact of advection and reaction terms on the solution profiles for various space and time fractional order derivatives are shown graphically for different particular cases. A drive has been made to study the convergence of the proposed scheme, which has been applied on the proposed mathematical model.