Comparison of five numerical schemes for fractional differential equations.

*(English)* Zbl 1128.65105
Sabatier, J. (ed.) et al., Advances in fractional calculus. Theoretical developments and applications in physics and engineering. Dordrecht: Springer (ISBN 978-1-4020-6041-0/hbk; 978-1-4020-6042-7/e-book). 43-60 (2007).

Summary: This paper presents a comparative study of the performance of five different numerical schemes for the solution of fractional differential equations. The schemes considered are a linear, a quadratic, a cubic, a state-space noninteger 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 problem. 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

##### MSC:

65R20 | Integral equations (numerical methods) |

26A33 | Fractional derivatives and integrals (real functions) |

45J05 | Integro-ordinary differential equations |