The fractional order Euler polynomials are introduced to obtain the solution of the class of space fractional diffusion equations. This is an innovative method for solving space fractional differential equations among the fractional calculus. These properties are utilized to transform the partial differential equation to algebraic equations with unknown Euler coefficients. The fractional derivatives are described based on the Caputo sense by using Riemann--Liouville fractional integral operator. A new hybrid function approximation based on fractional Euler polynomials and the algebraic polynomial has been initiated. The solution obtained by our method coincides with the solution obtained through other methods mentioned in the literature. Finally, several numerical examples are given to illustrate the accuracy and stability of this method.