Fractional model for simulating Long-Term fracture conductivity decay of shale gas and its influences on the well production

•A fractional model for simulating long-term fracture conductivity decay was developed.•The damage rate of cumulative production induced by shale creep is unignorable.•The formation viscous modulus determines the strength of shale viscoelastic mechanical behaviors.•Cumulative production damage rate caused by shale creep is obvious when formation viscous modulus is less than 30GPa.