<p>In this article, a new class of basis functions called generalized Laguerre polynomials is introduced to solve equations in the form of the non-linear time fractional reaction-diffusion equation. To obtain a new numerical method, the fractional derivative in the equation is replaced using Caputo’s definition. Then, using operational matrices of fractional and ordinary derivatives, in order to improve the presented numerical method, the method of generalized Laguerre polynomials (GLPs) is introduced. The basis of obtaining an approximate solution in this method is that the approximate solution is considered as a linear combination of these basic functions in terms of coefficients and control parameters. By obtaining the values of coefficients and control parameters optimally using the method of Lagrange cofficients, the approximate solution is obtained. The advantage of this method is to use a small number of basis functions to obtain satisfactory results. On the other hand, the accuracy of the method is improved by increasing the number of sentences of basic functions. In the end, with the aim of confirming the correctness of the numerical results and proving the efficiency, we will test the GLPs method by presenting two examples. </p>