The fractional calculus approach in the constitutive relationship model of viscoelastic fluid was introduced. The velocity and temperature fields of the vortex flow of a generalized second fluid with fractional derivative model were described by fractional partial differential equations. Exact analytical solutions of these differential equations were obtained by using the discrete Laplace transform of the sequential fractional derivatives and generalized Mittag-Leffler function. The influence of fractional coefficient on the decay of vortex velocity and diffusion of temperature was also analyzed.