A rock creep model based on Atangana-Baleanu fractional derivative with coupled damage effects of pore water pressure, stress and time

•The expression of rock damage variable is established by studying the law of rock damage considering the influence of pore water pressure, stress and time.•A new pore water pressure-stress-time coupled damage fractional (PSTCDF) creep model is established based on the Atangana-Baleanu fractional derivative.•The rationality, validity and generalization of the PSTCDF model are proved by the analysis of the goodness of fit and generalization accuracy of the model to the experimental data.