Determination of the Frequency-Amplitude Relation for Nonlinear Oscillators with Fractional Potential Using He's Energy Balance Method

A He's Energy balance method (EBM) is used to calculate the periodic solutions of nonlinear oscillators with fractional potential. Some examples are given to illustrate the effectiveness and convenience of the method. We find this EBM works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the Exact or other analytical solutions has been demonstrated and discussed. Comparison of the result obtained using this method with that obtained by Exact or other analytical solutions reveal that the EBM is very effective and convenient and can therefore be found widely applicable in engineering and other science.

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