A closed-form non-stationary solution of fractional systems with order 1/2 subjected to stochastic excitation

Abstract

Abstract: This paper develops a novel method for determining a closed-form non-stationary stochastic response of linear systems with fractional derivative order 1/2 and subjected to stationary stochastic excitation. This is achieved by relying on the Laplace transform-based method for the linear fractional system, where the closed-form solution of the pulse response function is obtained by the eigenvector expansion of the state-space equation of the linear system with fractional derivative order 1/2. Pertinent Monte Carlo simulations demonstrate the applicability and accuracy of the proposed method.

keywords: Fractional derivative, eigenvector expansion, Laplace domain, non-stationary response, Pole and residue