In this paper, we develop a numerical method by using operational matrices based on Hosoya polynomials of simple paths to find the approximate solution of di usion equations of fractional order with respect to time. This method is applied to certain di usion equations like time fractional advection-di usion equations and time fractional Kolmogorov equations. Here we use the Atangana-Baleanu fractional derivative. With the help of this approach we convert these equations to a set of algebraic equations, which is easier to be solved. Also, the error bound is provided. The obtained numerical solutions using the presented method are compared with the exact solutions. The numerical results show that the suggested method is convenient and accurate
