(in lingua inglese)
The achievement of this work is to apply the CM and NUM in order to study the strongly nonlinear differential equation with fractional power that governed from the unsteady motion of vertically falling spherical particles in a power-law non-Newtonian fluid. The current method was applied without any discretization, restrictive assumptions, or transformation. Also, this method can be used to develop valid solutions even to problems that are highly nonlinear and may be considered as an important and significant refinement of the formerly developed methods.