The Simulation Technique for Fractional Order Systems with Nonzero Initial Value

The paper mainly concerns about nonzero initial value problems of fractional order dynamic systems. Firstly, to solve the limitation of the existing Simulink block diagram scheme with Riemann-Liouville definition, a modified modular approach is proposed. It is based on the improved piecewise approximation for fractional differential operator and integral operator. The method can solve the problem not only under Riemann-Liouville definition, but also Caputo definition. Considering that the fractional integral operator is supposed to own pure integral property, we construct the strict regular approximation model to improve the performance of the origin scheme. Then the method is simplified with the adoption of the state-space model. The effectiveness and the superiority of proposed schemes are verified by detailed fractional order differential equations.