The benchmark problems for the assessment of numerical algorithms on fractional-order differential equations

There are many numerical algorithms for solving the fractional-order differential equations (FODEs). The numerical algorithms are very different, and it is difficult to compare their performances. To solve this problem, some different FODEs with the known analytical solution are designed and proposed, they could be used as the benchmark problems for testing the numerical algorithms. A Simulink block diagram scheme is proposed for solving these benchmark problems, and the computing errors and the running times are reported. These benchmark problems and the solutions are constituted as a framework, and the numerical algorithms for solving the FODEs could be compared in the same framework. The comparing result could assess which algorithm is better to a concrete FODE.