SubIval

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: t0Dαtx(t)≈ax(t)+b. (1) SubIval works so far for the Riemann-Liouville and Caputo definitions of the fractional derivative.