**6. Conclusions**

Fractional derivative in the field of hyperspectral studies are rarely reported, especially for field-measured ground hyperspectral data. We collected soil samples and hyperspectral data in May 2017. Grünwald–Letnikov fractional derivative was used to analyze the correlation coefficient between the available potassium content and the soil ground hyperspectral data and Landsat 8 multispectral satellite data. Simulation results display that the small difference between spectrum data was clearly described by fractional derivative. The maximum absolute correlation coefficient appeared in the fractional order for the ground hyperspectral data and Landsat 8 multispectral satellite data. Therefore, fractional derivative enriches the pre-processing method of spectral data, provides potential spectrum information, increases the correlation coefficient between spectral reflectance and available potassium content, and provides scientific support for local precision agriculture.

**Author Contributions:** C.F. designed the research and performed all the modeling. A.T. and H.X. collected the experiment data. S.G., X.Y. and H.X. participated in the data analyses. C.F. and A.T. were involved in drafting and revising the manuscript.

**Funding:** The authors would like to thank the financial support of National Natural Science Foundation of China (41861054 and 41671198), and Yunnan Province Science and Technology Department and Education Department Project (2017FH001-067 and 2017FH001-117), China.

**Conflicts of Interest:** The authors declare no conflict of interest.
