Affiliation:
1. Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan
2. Department of Mathematics, University of Karachi, Karachi–75270, Pakistan
Abstract
Abstract
The first problem of Stokes for an incompressible Oldroyd-B fluid with fractional derivatives is studied using Fourier sine and Laplace transforms. The solutions that have been obtained, unlike the known solutions from the literature, are presented as a sum between the Newtonian solutions and the non-Newtonian contributions. The non-Newtonian contributions, as expected, tend to zero for α = β and λ → λ
r
. Furthermore, the solutions for ordinary Oldroyd-B, fractional and ordinary Maxwell, fractional and ordinary second grade fluid, performing the same motion, are also obtained as limiting cases of general solutions. The present solution for ordinary Oldroyd-B and second grade fluids are verified by comparison with the previously well known results. Finally, the influence of material and fractional parameters on the fluid motion, as well as a comparison among fractional Oldroyd-B, fractional Maxwell, fractional second grade and Newtonian fluids, is also analyzed by graphical illustrations.
Subject
Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modeling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics
Cited by
13 articles.
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