Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 33122
Application of He-s Amplitude Frequency Formulation for a Nonlinear Oscillator with Fractional Potential
Abstract:
In this paper, He-s amplitude frequency formulation is used to obtain a periodic solution for a nonlinear oscillator with fractional potential. By calculation and computer simulations, compared with the exact solution shows that the result obtained is of high accuracy.
Keywords: He's amplitude frequency formulation, Periodic solution, Nonlinear oscillator, Fractional potential.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1082189
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[1] J.H. He, Variational approach for nonlinear oscillators, Chaos Solitons & Fractals 34(2007) 1430-1439.
[2] J.H. He, L.N. Zhang, Generalized solitary solution and compacton-like solution of the Jaulent-Miodek equations using the Exp-function method, Phys. Lett. A 372(7)(2008) 1044-1047.
[3] J.H. He, M.A. Abdou, New periodic solutions for nonlinear evolution equations using Exp-function method, Chaos Solitons & Fractals 34(5)(2007) 1421-1429.
[4] F. Xu, Application of Exp-function method to symmetric regularized long wave (SRLW) equation, Phys. Lett. A 372(3)(2008) 252-257.
[5] L. Xu, Variational approach to solitons of nonlinear dispersive K(m,n) equations, Chaos Solitons & Fractals 37(1)(2008) 137-143.
[6] J.H. He, Variational iteration method some recent results and new interpretations, J. Comput. Appl. Math. 207(1)(2007) 3.
[7] S.Q. Wang, J.H. He, Nonlinear oscillator with discontinuity by parameterexpansion method, Chaos Solitons & Fractals 35(2008) 688-691.
[8] J.H. He, Homotopy perturbation technique, Comput. Method. Appl. Mech. 178(1999) 257-262.
[9] J.H. He, Homotopy perturbation method: A new nonlinear analytical technique, Appl. Math. Comput. 135(2003) 73-79.
[10] J.H. He, The homotopy perturbation method for nonlinear oscillators with discontinuities, Appl. Math. Comput. 151(2004) 287-292.
[11] J.H. He, Comment on -He-s frequency formulation for nonlinear oscillators-, Eur. J. Phys. 29(2008) L1-L4.
[12] J.H. He, An improved amplitude-frequency formulation for nonlinear oscillators, Int. J. Nonlinear. Sci. Numer. Simul. 9(2)(2008) 211-212.
[13] T. Ozis, A. Yildirim, Determination of the frequency-amplitude relation for a Duffing-harmonic oscillator by the energy balance method, Comput. Math. Appl. 54(2007) 1184-1187.
[14] H.M. Liu, Approximate period of nonlinear oscillators with discontinuities by modified Lindstedt-Poincare method, Chaos Solitons & Fractals 23(2)(2005) 577-579.
[15] D.H. Shou, J.H. He, Application of parameter-expanding method to strongly nonlinear oscillators, Int. J. Nonlinear. Sci. Numer. Simul. 8(2007) 113-116.