Separation method of semi-fixed variables together with integral
bifurcation method for solving generalized time-fractional thin-film
equations
Abstract
It is well known that investigation on exact solutions of nonlinear
fractional partial differential equations (PDEs) is a very difficult
work compared with integer-order nonlinear PDEs. In this paper, based on
the separation method of semi-fixed variables and integral bifurcation
method, a combinational method is proposed. By using this new method, a
class of generalized time-fractional thin-film equations are studied.
Under two kinds of definitions of fractional derivatives, exact
solutions of two generalized time-fractional thin-film equations are
investigated respectively. Different kinds of exact solutions are
obtained and their dynamic properties are discussed. Compared to the
results in the existing references, the types of solutions obtained in
this paper are abundant and very different from those in the existing
references. Investigation shows that the solutions of the model defined
by Riemann-Liouville differential operator converge faster than those
defined by Caputo differential operator. It is also found that the
profiles of some solutions are very similar to solitons, but they are
not true soliton solutions. In order to visually show the dynamic
properties of these solutions, the profiles of some representative exact
solutions are illustrated by 3D-graphs.