Block Diagram Modeling and Simulation for Delay Fractional-Order Differential Equation

Delay fractional-order differential equations (DFODEs) are difficult to solve, this paper focuses on this kind of equations. Four DFODEs with known analytical solutions are designed, they can be regarded as benchmark problems. With the known analytical solution, the calculation error of the algorithm can be calculated easily. This is helpful for researchers to test their own numerical algorithms. In addition, a block diagram method is proposed for modeling and solving DFODEs, all the benchmark problems in this paper can be solved by this method. The maximum errors under different parameters are reported, these results illustrate that the block diagram method is accurate and effective for DFODEs.