Analytical solution for aqueous polymer solutions equation with a fractional time derivative by Adomian decomposition method

The objective of this paper is the elaboration of a methodological approach to investigate the unsteady motion of aqueous polymer solution with time fractional derivative in a tube. Adomian decomposition is used for this aim. The 1D radial component is first considered and the analytical solution is obtained in a general framework. Second, the radial and angular velocity coordinates are considered and the resulting nonlinear fractional partial differential system is investigated. The effects of fractional order and relaxation coefficients are analyzed. Explicit solution of the equation was given in an example that generalizes several cases and then reweighed graphically in particular known cases. The applied approach is simple and effective in terms of calculation time, efficient in terms of efficiency and simplicity.