**ABSTRACT**

Ground temperature is an important physical indicator reflecting the natural ecological environment of the Earth's surface. Soil spectrum is a comprehensive reflection of soil properties, but there are few studies on the prediction of ground temperature based on soil field spectrum using fractional calculus. In this paper, the fractional derivative is used to study the correlation between soil spectrum and ground temperature from zeroth order to second order, and the characteristic wavelength bands are extracted. Simulations show that the fractional approach can amplify the difference of the soil field spectral signal. The wavelength bands for the 0.01 significance test begin with 0.6th order, while the 1.3th order sees 33 wavelength bands. Coefficients of determination of 0.7, 0.8, 0.9, 1.3, 1.4, 1.5, 1.6, and 1.7-order are all greater than 0.66, indicating that the established model of linear stepwise multiple regression gives a better prediction.

**KEYWORDS**

PAPER SUBMITTED: 2018-12-16

PAPER REVISED: 2019-06-19

PAPER ACCEPTED: 2019-08-18

PUBLISHED ONLINE: 2020-06-21

**THERMAL SCIENCE** YEAR

**2020**, VOLUME

**24**, ISSUE

**4**, PAGES [2301 - 2309]

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