Abstarct: The purpose of this thesis is to introduce a new method using artificial neural networks for same of to the approximation solutions of fractional differential equations with the use fractional polynomial and fractional derivative. Classical polynomials such as Legendre, Lagrange and Chebyshev have played a very important role in solving the problems of classical differential equations. These polynomials have correct powers. The fractional derivative of these polynomials is a function of fractional powers. This feature will reduce the error by increasing the number of polynomials. One of the effective methods for solving the problems of fractional calculus is the use of baxse functions as 〖 Φ〗_n=∑_(i=0)^n▒c_i x^iα. For this purpose, in this thesis, polynomials are baxsed on the approximation of the fractional differential equations with the artificial neural networks. First, we use classical polynomials as the baxse with a caputo-fabrizio derivative and then use fractional polynomials for the baxse with a caputo derivative artificial neural networks. Finally, the numerical simulation of the efficiency of the method is shown.