An Approximate Method for Solving a Vibration Equation Involving Fractional Derivatives

摘要

The response of one-degree-of-freedom systems with fractional distributed-order damping is studied. The dynamics of such systems constitutes the problem of the fractional distributed-order oscillator. This paper presents a new numerical method for solving this fractional distributed order oscillator. The method is based on using fractional Taylor vector approximation. The operational matrix of the fractional integration for fractional Taylor vector is given and is utilized to reduce the solution of the fractional distributed order oscillator to a system of algebraic equations. An illustrative example is included to demonstrate the validity and applicability of this technique.