This paper presents a study of visco-elastic flow of an incompressible generalized Oldroyd-B fluid between two infinite parallel plates in which the constitutive equation involves fractional order time derivative. The solutions of field equations are being obtained for the motion of the said fluid between two parallel plates where the lower plate starts to move with steady velocity and the upper plate remains fixed in the first problem and the upper plate oscillates with constant frequency and the other being at rest in the second problem. The exact solutions for the velocity field are obtained by using the Laplace transform and finite Fourier Sine transform technique in terms of Mittag Leffler and generalised functions. The analytical expression for the velocity fields are derived and the effect of fractional parameters upon the velocity field is depicted graphically.

In this paper an attempt has been made to study the unsteady incompressible flow of a genera-

This paper investigates the convective flow of an incompressible viscous electrically conducting second grade fluid through a porous medium occupying a semi-infinite region over an oscillating porous plate in presence of a transverse magnetic field with suction. The field equations for the velocity and temperature fields are solved analytically and the expressions for the velocity field, temperature field, skin friction and heat flux are obtained. The effects of permeability parameter, magnetic parameter/Hartmann number, Prandtl number, heat source parameter and suction parameter on the velocity field are illustrated graphically. The influence of suction parameter, Prandtl number and heat source parameter on temperature field is analyzed with the help of figures. Furthermore the effects of permeability parameter and magnetic parameter on skin friction are shown diagrammatically.

Incompressible viscous fluid flow through a porous medium between two infinite parallel plates with moving upper plate in a rotating system has been studied here. The exact solution of the governing equation for the velocity field has been obtained by using Laplace and finite Fourier sine transformations in series form in terms of Mittage-Leffler function. It can be found that the fluid velocity decreases with the increasing values of fractional calculus parameter α and the permeability of the porous medium K. It can be also observed that the fluid velocity increases with the higher values of the viscosity of the porous medium. The dependence of the velocity field on fractional calculus parameters as well as material parameters has been illustrated graphically.

The unsteady incompressible viscous flow of a Generalised Maxwell fluid between two coaxial rotating infinite parallel circular disks is studied by using the method of integral transforms. The motion of the fluid is created by the rotation of the upper and lower circular disks with different angular velocities. A fractional calculus approach is utilized to determine the velocity profile in series form in terms of Mittag-Leffler function. The influence of the fractional as well as the material parameters on the velocity field is illustrated graphically.