Fractional lower order moments (FLOMs) based on the non-Gaussian stable distribution are employed for texture classification and synthesis. The parameters of a 2-D autoregression model are estimated using the fractional lower order moments, and these parameters are used for texture classification. The analysis of FLOMs is useful when the variance of the underlying distribution is not finite and thus when the whole second-order statistics theory fails; hence, parameter estimation using FLOMs gives a more robust model over the existing methods that use autocorrelation function. This stable distribution is used in the synthesis of texture, and the performance of FLOMs and the autocorrelation methods are compared. By extensive simulations it is shown that the FLOM-based feature extraction algorithm outperforms the autocorrelation-based one.