Abstract: Fractional calculus extends the conception of integer calculus to the fractional order. This study set Wucaiwan open coalmine area in the Eastern Junggar Basin in Xinjiang Uygur Autonomous Region as the study area, the arsenic (As) element content and spectral reflectance of the soil samples were measured. The paper treated the hyperspectral reflectance data ( R ) with 3 mathematical transforms such as \sqrtR, 1 / R, \ln (R), then the formula of Grünwald-Letnikov fractional derivative was used to calculate their 0 \sim 2 order derivative(interval 0.2 order), and the inversion effects were compared after the models between different transforms and the As content in soil were set up by PLSR. Results show that the model based on \sqrtR 1.8 order derivative transform \left(\mathrmRMSEC=1.996, \mathrmR_\mathrmC^2=0.821, \mathrmRMSEP=1.973, \mathrmR_\mathrmP^2=0.890, \mathrmRPD=\right. 2.367) is much better than others, and has a better capability to predict As content in soil. The results of this research would provide a reference basis for the application of fractional order derivative in monitoring heavy metal contamination by using hyperspectral data.