Abstract
The concern of the present research is to explore the fractionalized Oldroyd-B fluid with the influence of MHD effect, enclosed by two endless uniaxial circular cylinders, by utilizing Laplace transform with Antangano Baleanu factional operator and finite Hankel transform. Both cylinders are moving together about its same axis. The movement is produced by the inner and outer cylinders from rest, as a result of the rotational together with translational time-dependent velocities. The analytical outcomes of flow rate and corresponding to the tangential stress are introduced by integral and series pattern in form of the generalized function M. The solutions that have been satisfying all impose account conditions. The comparable solutions can easily be achieved for ordinary Oldroyd-B, Maxwell, second grade as well as Newtonian fluid, as exclusive cases of the generalized results. In the end, the graphical illustration depicted, to predict the impact of the relaxation time and non-integer order fractional material on the fluid flow, as well as comparison between the equations.