Journal of Applied Fluid Mechanics1735-357210520170901Oscillating Motion of an Oldroyd-B Fluid with Fractional Derivatives in a Circular Cylinder1421142653010.18869/acadpub.jafm.73.242.27079ENN.RazaDepartment of Mathematics, University of the Punjab, Quaid-e-Azam CampusE. U.HaqDepartment of Mathematics and Statistics, The University of LahoreM. M.RashidiUniversity of Birmingham, School of Civil Engineering, BirminghamA. U.AwanDepartment of Mathematics, University of the Punjab, Quaid-e-Azam CampusM.AbdullahDepartment of Mathematics, University of Engineering and TechnologyJournal Article19700101The velocity field and tangential shear stress for unsteady flow of an Oldroyd-B fluid with Caputo fractional derivatives through an infinite long cylinder are evaluated. The fluid in the infinitely long cylinder is initially at rest and at t = 0+, due to shear, the fluid starts to oscillate longitudinally. We have solved the fractional model with the tool of Laplace and finite Hankel transformations. The solutions are in series form and are written in generalized G-function to avoid the entanglement. In limiting cases, the solutions of ordinary Oldroyd-B fluid, Maxwell fluid with fractional as well as ordinary and Newtonian fluid are derived. Finally, behavior of different physical parameters on fluid is illustrated by graphs.https://www.jafmonline.net/article_530_59fe1fecd64fcc197fdb5ff096b568f5.pdf