Numerical comparison for the solutions of anharmonic vibration of fractionally damped nano-sized oscillator

In this paper, we consider the nonlinear vibrations of nano-sized cantilever. The elastic force is considered anharmonic, deriving from a Morse potential and the nonlinearity is attributed to the Casimir force. The solution is established for viscous and fractional damping by making use of He’s polynomials which are calculated from homotopy perturbation method (HPM). The solution procedure explicitly reveal the complete reliability and simplicity of the proposed algorithm. Moreover, comparison with variational iteration method (VIM) shows that both the techniques are in full agreement with each other.