A novel fractional model based on the Riemann Liouville fractional derivative to simulate the thermal performance of conventional solar still and show the effect of using hybrid nanofluid on the desalination system is presented. The results of the fractional model are compared with the results obtained from the classical model, then compared to real experimental data under various climate conditions of Upper Egypt. The theoretical results reveal a perfect agreement between the proposed fractional model and the experimental data of the still with a percentage of error reached 1.486% in summer and 3.243% in winter compared to an error percentage of 24.1 % and 20.08%,  in case of applying the classical. Moreover, the performance of the modified solar still after adding hybrid nanoparticles is also compared with the conventional solar still. The model is implemented using a hybrid nanofluid of alumina and copper oxide (Al₂O₃-CuO) with a concentration of 0.025% for each nanoparticle. The results show that using hybrid nanofluid raises the still daily productivity to 5.5239 kg/m².day in summer and 3.1079 kg/m².day in winter of an enhancement in the still output yield of 27.2% and 21.7% compared with still without nanoparticles. The average energy efficiency of the still in summer is also increased to 49.54% and 23.212% in summer and winter, respectively, with an augmentation of 12.6% and 11.85% in hot and cold climate conditions, respectively. In addition, the average exergy efficiency is raised by 22.5% in summer and 13.4% in winter by using hybrid nano.