Variational principle for nonlinear oscillator arising in a fractal nano/microelectromechanical system

In this work, a nonlinear oscillator model with a fractal derivative is successfully established for a fractal nano/microelectromechanical system (MEMS), and its variational principle is obtained by the semi-inverse method. The established variational formulation suggests an energy conservation for the fractal nonlinear oscillator, and its approximate analytical solution is found by the two-scale transform and homotopy perturbation method; Laplace transform is used in the solution process. This paper sheds a new light on fractal MEMS.