A novel multi-phase-lags model with fractional order derivative is introduced to study a thick hollow cylinder with two temperatures under the influence of magnetic field and rotation. The basic non-dimensional equations of the problem are discussed by using harmonic wave analysis. Numerical computations are carried out with the help of Matlab software. Comparisons are made with the results of the refined-phase-lag theory for different values of rotation and magnetic field. Comparisons also are made with the results of the refined-phase-lag theory for different values of the fractional order parameter. Some particular cases of special interest have been deduced from the present investigation.