Current version: 1.03 (updated 2018-03-28)
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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}}
+ b


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



  1. M.Sowa: “A subinterval-based method for circuits with fractional order elements”. Bull. Pol. Acad. Sci., Tech. Sci. 2014 vol. 62 no. 3, pp. 449-454 (2014).
  2. M.Sowa: “Application of SubIval in solving initial value problems with fractional derivatives”, Applied Mathematics and Computation 319, 86-103 (2018).