期刊名称：International Journal of Differential Equations
印刷版ISSN：1687-9643
电子版ISSN：1687-9651
出版年度：2011
卷号：2011
DOI：10.1155/2011/193813
出版社：Hindawi Publishing Corporation
摘要：Unsteady flow of an incompressible Maxwell fluid with fractional derivative induced by a sudden moved
plate has been studied, where the no-slip assumption between the wall and the fluid is no longer valid. The solutions
obtained for the velocity field and shear stress, written in terms of Wright generalized hypergeometric functions 𝑝Ψ𝑞,
by using discrete Laplace transform of the sequential fractional derivatives, satisfy all imposed initial and boundary
conditions. The no-slip contributions, that appeared in the general solutions, as expected, tend to zero when slip
parameter is 𝜃→0. Furthermore, the solutions for ordinary Maxwell and Newtonian fluids, performing the same motion,
are obtained as special cases of general solutions. The solutions for fractional and ordinary Maxwell fluid for
no-slip condition also obtained as limiting cases, and they are equivalent to the previously known results. Finally,
the influence of the material, slip, and the fractional parameters on the fluid motion as well as a comparison among
fractional Maxwell, ordinary Maxwell, and Newtonian fluids is also discussed by graphical illustrations.
