Current version: 1.03 (updated 2018-03-28)
Useful? Please cite either [1] or [2].

(Update 2019-02-22) Octave and Matlab solvers (version 1.01) that can be applied for nonlinear problems available here. A detailed description on their usage is given in the respective .m files.

SubIval (the subinterval-based method; first appearance in [1]) is a numerical method for computations of the fractional derivative in IVPs (initial value problems). In a computed time step its usage results in an implicit formula much like one that can be obtained then applying an implicit BDF (backward differentiation formula) for a first order derivative.
The formula resulting from SubIval is:

$$_{t_{0}} \mathrm{D} _{t} ^{\mathrm{\alpha}} x(t) \approx ax(t) + b .$$

(1)

SubIval works so far for the Riemann-Liouville and Caputo definitions of the fractional derivative.