Solving the nonlinear equations for one-dimensional nano-sized model including Rydberg and Varshni potentials and Casimir force using the decomposition method

The Adomian decomposition method has been applied to solve the nonlinear equations from the one-dimensional model for a nano-sized-oscillator. The model includes Rydberg and Varshni potentials as well as Casimir force with fractional damping. New approximate solution of the equations of motion for anharmonic vibrations of a nano-sized oscillator with the elastic force deriving from the Rydberg and Varshni potentials has been obtained.