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Analysis of fundamental solutions to fractional diffusion-wave equation in polar coordinates

Povstenko Y.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2009

Vol. 14

97-104

The diffusion-wave equation is a mathematical model of a wide range of important physical phenomena. The first and second Cauchy problems and the source problem for the diffusion-wave equation are considered in cylindrical coordinates. The Caputo fractional derivative is used. The Laplace and Hankel transforms are employed. The results are illustrated graphically.

Some exact solutions for the rotational flow of a generalized second-grade fluid between two circular cylinders

Mahmood A., Saifullah, Bolat G.

Archives of Mechanics

2008

Vol. 60, nr 5

385-401

The velocity field and the associated tangential stress corresponding to the flow of a generalized second-grade fluid between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. At time t=0, the fluid is at rest and at t=0+ the cylinders suddenly begin to rotate about their common axis with a constant angular acceleration. The solutions that have been obtained satisfy the governing differential equations and all the imposed initial and boundary conditions. The similar solutions for a second-grade fluid and Newtonian fluid are recovered from our general solutions. The influence of the fractional coefficient on the velocity of the fluid is also analyzed by graphical illustrations.