A NUMERICAL ALGORITHM FOR DIFFERENTIAL EQUATIONS WITH NONLINEAR FRACTIONAL DERIVATIVES

A numerical integration algorithm to solve single-degree of freedom (1-DOF) nonlinear fractional differential equations (NFDEs) is developed by the use of the one stepscheme; Newmark-β method. The NFDE involving the fractional derivatives of the displacement and the displacement squared is numerically solved by the proposed numerical integration algorithm. In this paper, the derivation of the numerical integration algorithm, the error analysis of the algorithm, and the contribution of the displacement squared fractional derivative term on the solution of the NFDE are given.