In the present article, an efficient operational matrix based on the famous Laguerre polynomials is applied for the numerical solution of two-dimensional non-linear time fractional order reaction–diffusion equation. An operational matrix is constructed for fractional order differentiation and this operational matrix converts our proposed model into a system of non-linear algebraic equations through collocation which can be solved by using the Newton Iteration method. Assuming the surface layers are thermodynamically variant under some specified conditions, many insights and properties are deduced e.g., nonlocal diffusion equations and mass conservation of the binary species which are relevant to many engineering and physical problems. The salient features of present manuscript are finding the convergence analysis of the proposed scheme and also the validation and the exhibitions of effectiveness of the method using the order of convergence through the error analysis between the numerical solutions applying the proposed method and the analytical results for two existing problems. The prominent feature of the present article is the graphical presentations of the effect of reaction term on the behavior of solute profile of the considered model for different particular cases.

中文翻译：

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二维非线性时间分数阶反应-扩散方程在多孔介质多组分流体亚扩散过程中的应用

在本文中，基于著名的拉盖尔多项式的有效运算矩阵应用于二维非线性时间分数阶反应扩散方程的数值解。为分数阶微分构造运算矩阵，该运算矩阵通过搭配将我们提出的模型转换为非线性代数方程组，可以使用牛顿迭代法求解。假设表面层在某些特定条件下在热力学上是可变的，则可以推导出许多见解和性质，例如与许多工程和物理问题相关的非局部扩散方程和二元物种的质量守恒。本手稿的显着特点是找到了所提出方案的收敛性分析，并通过应用所提出方法的数值解与两个分析结果之间的误差分析，使用收敛阶数验证和展示了该方法的有效性。存在的问题。本文的突出特点是反应项对不同特定情况下所考虑模型的溶质分布行为的影响的图形表示。