Solving Bagley-Torvik Equation Based on Simulink Circuit Simulation

Abstract:

A novel solution method, circuit simulation method, is proposed for the BagleyTorvik equation with constant coefficient. The core idea of this method is to construct microproduct operator: sμ(－1＜μ＜0) by the classical fractional approximation circuit to replace the fractional derivative:0Dμt(－1＜μ＜0). The circuit simulation method converts the impedance function of impedance approximation circuit into the transfer function module in Simulink which is then used to build the simulation block diagram to solve the fractional differential equation. Comparing the circuit simulation method with the traditional numerical method, namely the numerical approximation method and the Green's function method. The comparison results show that the solving results of circuit simulation method is stable and reliable, and the actual circuit based on the simulation block diagram can be built to solve the fractional differential equation in real time.