Comparison of five numerical schemes for fractional differential equations

This paper presents a comparative study of the performance of five different numerical schemes for the solution of fractional differential equations. The schemes considered axe a linear, a quadratic, a cubic, a state-space non-integer integrator, and a Direct discretization method. Results are presented for five different problems which include two linear 1-D, two nonlinear 1-D and one linear multidimensional. Both homogeneous and nonhomogeneous initial conditions (ICs) are considered. The stability, accuracy, and computational speeds for these algorithms are examined. Numerical simulations exhibit that the choice of a numerical scheme will depend on the problem considered and the performance criteria selected.