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 (DTM), 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 aa (eigenvalue parameter), LL (length) and αα (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.