In this work, we introduce a numerical method for solving nonlinear fractional system of Lane–Emden type equations. The proposed technique is based on Dickson operational matrix of a fractional derivative. First, we deduce the Dickson operational matrix of the fractional derivative using Dickson polynomial, and then, the obtained matrix is unitized to convert the fractional Lane–Emden system with its initial conditions into a system of nonlinear algebraic equations. This system of algebraic equations can be solved numerically via Newton’s iteration method. An error estimate of the proposed method is derived. Numerical examples are provided to demonstrate the validity, applicability, and accuracy of the new technique.

在这项工作中，我们介绍了一种求解Lane-Emden型方程非线性分数系统的数值方法。所提出的技术基于分数导数的Dickson运算矩阵。首先，我们使用Dickson多项式推导分数导数的Dickson运算矩阵，然后将获得的矩阵统一起来，将具有初始条件的分数Lane-Emden系统转换为非线性代数方程组。该代数方程组可以通过牛顿迭代法进行数值求解。得出了所提出方法的误差估计。数值例子说明了该新技术的有效性，适用性和准确性。