In this paper, a fractional model of the conventional solar desalination system (solar still) is presented based on three different operators of fractional derivatives (Riemann Liouville, Atangana-Baleanu, and Caputo-Fabrizio). A comparison between the new model, the experimental data, and the classical model on the performance of single slope solar still is discussed under cold climate conditions of upper Egypt. The simulation results reveal good agreement between the fractional model and the experimental results with a maximum error of 3.423% in cold climate conditions, compared to 20.08% for the classical model.