Analytical methods for solving the time-fractional Swift-Hohenberg (S-H) equation
In this paper, the most effective methods, the homotopy perturbation method (HPM) and the differential transform method (DIM), are applied to obtain the approximate solutions of the nonlinear time-fractional Swift-Hohenberg (S-H) equation. The basic philosophy of these methods does not involve linearization, weak nonlinearity assumptions or perturbation theory. Numerical solutions for various combinations of the parameters a (eigenvalue parameter), L (length) and alpha (fractional index) are obtained. The solutions of the S-H equation are useful for studies of shear thinning effects in non-Newtonian fluid flows. At the end, the solutions obtained are also presented graphically. (C) 2010 Elsevier Ltd. All rights reserved.
swift-hohenberg (s-h) equation homotopy perturbation method (hpm) analytical solution differential transform method (dtm) fractional differential equations (fde)