Application of Hamiltonian Approach to the Generalized Nonlinear Oscillator with Fractional Power

作者：Cveticanin L^*; Kalami Yazdi M; Saadatnia Z; Askari H

来源：International Journal of Nonlinear Sciences and Numerical Simulation, 2010, 11(12): 997-1002.

• Hamiltonian Approach procedure
• fraction order nonlinear oscillator

Hamiltonian Approach (HA) is adopted to solve the generalized nonlinear equations with integer and non-integer (fractional) power terms: (sic)x + Sigma(i)c(i)(2)x vertical bar x vertical bar(alpha i-1) = 0, where alpha i is a positive fraction or positive integer. Approximate analytical solution is obtained and consequently the relationship between the natural frequency and the initial condition is derived. An error analysis is carried out and accuracy and validity of the approximate solution are then verified. Numerical simulations cover a range of large amplitudes of oscillation and accordingly it is shown that the approximate solutions are quite reliable even for strong nonlinearities.

• 出版日期2010-12