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.

在本文中，使用移位勒让德-高斯-洛巴托搭配法 （SLGLCM） 求解具有初始和边界条件的非线性耦合二维时空分数阶反应-平流-扩散方程 （2D-STFRADEs），其中分数阶导数定义为 Caputo 意义。SLGLC 方案用于将耦合的非线性 2D-STFRADE 离散化为移位的勒让德多项式根，以将其转换为代数方程组。该方案的效率和效果通过错误分析得到确认，同时将该方案应用于具有精确解决方案的两个现有问题。对于不同的特定情况，平流和反应项对各种空间和时间分数阶导数的解曲线的影响以图形方式显示。人们一直在努力研究所提出的方案的收敛性，该方案已应用于所提出的数学模型。