Abstract: Fourier series expansion (FSE) plays a pivotal role in frequency domain analysis of a wide variety of nonlinear dynamical systems. To the best of our knowledge, there are two general approaches for FSE, i.e., a collocation ...

Abstract: This paper presents an accurate and efficient hybrid solution method, based on Newmark-β algorithm, for solving nonlinear oscillators containing fractional derivatives (FDs) of arbitrary order. Basically, this method employs ...

Abstract: This paper presents an investigation on the free vibration of an oscillator containing a viscoelastic damping modeled by fractional derivative (FD). Based on the fact that the vibration has slowly changing decay rate and ...

Abstract: It has been a difficult task to solve fractional oscillators analytically, especially when variableorder fractional derivatives (FDs) are included. The major difficulty consists in deriving analytical expressions for the ...