(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 ) 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:
SubIval works so far for the Riemann-Liouville and Caputo definitions of the fractional derivative.
- 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).
- M.Sowa: “Application of SubIval in solving initial value problems with fractional derivatives”, Applied Mathematics and Computation 319, 86-103 (2018).