Abstract: Prone tothe staircase effect and the blurring of the traditional variational image magnification, on the basis of considering the non convex order two total generalized variation in the suppression of the staircase effect and the fractional order in preserving the image details the characteristics of non convex total two order generalized variational model of fractional texture image magnification based on decomposition is proposed. The new model decomposes the low resolution image into two parts: cartoon and texture, because for a flat area, easy to produce the staircase effect, so the cartoon part uses the two order non convex total generalized variational model. In this paper, the fractional variational model is used to deal with the texture of the image with more details. In this paper, the primal dual and Chambolle projection algorithm are used to solve the new fractional non convex model. The results of numerical experiments show that the new model has a significant improvement in peak signal to noise ratio and mean square error.