An exact solution of start-up flow for the fractional generalized Burgers’ fluid in a porous half-space

Modified Darcy’s law for fractional generalized Burgers’ fluid in a porous medium is introduced. The flow near a wall suddenly set in motion for a fractional generalized Burgers’ fluid in a porous half-space is investigated. The velocity of the flow is described by fractional partial differential equations. By using the Fourier sine transform and the fractional Laplace transform, an exact solution of the velocity distribution is obtained. Some previous and classical results can be recovered from our results, such as the velocity solutions of the Stokes’ first problem for viscous Newtonian, second grade, Maxwell, Oldroyd-B or Burgers’ fluids.