Benchmark problems for Caputo fractional-order ordinary differential equations

There are many numerical algorithms for solving the fractional-order ordinary differential equations (FODEs). They are usually very different in nature, and it is difficult to compare their performances. To solve this problem, a set of five benchmark problems of different categories of FODEs with known analytical solution are designed and proposed, they can be used as benchmark problems for testing the numerical algorithms. A Simulink block diagram scheme is used for solving these benchmark problems, with computing errors and the running times reported.