Soil organic matter (SOM) plays an important role in ameliorating environmental problems such as land salinization, desertification, and grassland degradation in arid areas. To explore the feasibility of the fractional differential method in hyperspectral SOM inversion, 73 soil samples from Weigan River to Kuqa River oasis were considered as research objects. By measuring the SOM content and spectral reflectance, the mathematical transformation of a fractional differential of order 0-2 was performed using a 0.2-order differential as the step size. Further, the correlation between the fractional processing spectrum and SOM content was analyzed. Support vector machine regression, partial least squares regression, and random forest (RF) methods were used to quantitatively invert the SOM content. The results reveal that the prediction accuracy of the SOM inversion model established by the 1.2 RF derivative is the highest, with Coefficient of determination of 0.93, Root mean squared error of 1.62, and Relative percent difference of 3.65. These results can provide a basis for accurate inversion of SOM in this study area, and they also have a certain reference significance for inversion of SOM in other areas.