Abstract: Firstly, based on techniques such as  Taylor expansion and Chapman-Enskog multi-scale expansion,  the lattice Boltzmann method was used to accurately recover the discussed macroscopic equations, and  the equilibrium distribution function expressions of D1Q3 and D2Q9 models were derived. Secondly,  two numerical examples were used to verify the effectiveness of the proposed method. The results show that the lattice Boltzmann method can be used to solve the numerical solution of the Caputo type modified time fractional equation.

Key words: Caputo type fractional , equation, lattice Boltzmann method, reaction diffusion equation, discretization of fractional equation