A numerical integration algorithm to solve single-degree-of-freedom nonlinear fractional differential equations (NFDEs) is proposed, by introducing the power time concept and by means of the Newmark-β method one step scheme. An NFDE involving fractional derivatives of the displacement and the displacement squared is solved numerically, using the proposed power time algorithm. The error analysis of the algorithm, and the contribution of the displacement squared fractional derivative term to the solution of NFDE, are also given.
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