Abstract
A numerical algorithm to solve a nonlinear fractional differential equation (NFDE) which includes the fractional derivative of the first and the second power or displacement is developed. These displacements are related to the linear and the nonlinear dynamical viscoelastic behavior. Derivation of the numerical integration algorithm by the use of one-step scheme of Newmark-β method, error evaluation and some important parameter studies for a typical numerical model are given. The characteristics of the linear and the nonlinear fractional derivative responses for ramp input, and of the nonlinear viscoelastic responses of the NFDE for sinusoidal input are investigated. From the study, the developed numerical algorithm is validated to solve the NFDE.
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