Stability analysis for a single degree of freedom fractional oscillator

Abstract

This paper investigates the analytical solution, asymptotical stability and BIBO stability of a single degree of freedom (SDOF) fractional oscillator. By applying the Laplace transform, an analytical solution is provided in terms of Prabhakar’s function. With the decomposition of state–space, an equivalent incommensurate fractional differential system is obtained. New criteria on the asymptotical stability and BIBO stability are derived based on the distribution of the characteristic roots and the poles, respectively. An example under three diverse cases is presented to illustrate the validity and flexibility of our main results and the memory and hereditary effects of the fractional orders.