The __SubIval.dll__ ActiveX library was written in C# and can be therefore executed in any other program with .NET support.

As for popular CAS (Computer Algebra Systems) where one would like to compute the fractional derivative in an initial value problem – SubIval.dll has been verified to work with GNU Octave, Matlab, FreeMat (32-bit) and Mathematica.

The examples for Octave, Matlab and FreeMat are now set up so that they call

an FDE solver (descriptions to the codes will be added in the near future).

Exemplary codes:

**[Octave/Matlab files]** **[FreeMat (32-bit) files]** **[Mathematica code]**

*(The Mathematica code is given in a text file as the tests have been made on a trial version and comments have been added after the trial had expired).
*

*(The FreeMat code applies the SubIvalC.dll library).*

*(For Octave/Matlab SubIval.dll needs to be registered – this can be done easily by simply running the attached RegisterSubIval.exe file. The solver runs the actxserver function, which requires the DLL to be registered).*

The codes implement a time stepping solver with an adaptive step-size 2 stage scheme. where the fractional derivative is approximated through the SubIval library. Four exemplary problems are introduced in the scripts (which one is solved is determined by the

**variable), they have been introduced in [1, 2, 3].**

`example`

If you want to solve another problem (no matter if purely mathematical or resulting from circuit theory) and need advice on the configuration then do not hesitate to contact the author (

**marcin.sowa@polsl.pl**).

If you will find the SubIval.dll useful and publish some results then please cite [1] and/or [2].

The first problem already implemented in the codes is a simple

*RLC*circuit depicted in Figure 1.

The second problem (introduced in [2]) is one of an AC circuit with fractional order coils and capacitors (Figure 2).

The third problem (will be introduced in [3], motivated by [4]) deals with a

*RC*ladder network (Figure 3).

The fourth problem (will be introduced in [3]) is another AC circuit with fractional capacitors and coils (Figure 4).

Fig.1. *RLC* circuit problem with fractional capacitor and fractional coil [2]

Fig.2. AC circuit problem with fractional capacitors and fractional coils [2]

Fig.3. *RC* ladder circuit with fractional capacitors [3] (motivated by [4])

Fig.4. AC circuit problem with fractional capacitors and fractional coils [3]

### References

- 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 (Impact Factor 0.914) (2014).
- M.Sowa: “Application of SubIval, a method for fractional-order derivative computations in IVPs” in Theory and applications of non-integer order systems. Springer International Publishing, 2017, pp. 489-499 in series: Lecture Notes in Electrical Engineering vol. 407 (2017).
- M.Sowa: “Application of SubIval in solving initial value problems with fractional derivatives”. Applied Mathematics and Computation 319, 86-103 (2018).
- W. Mitkowski, P. Skruch: “Fractional-order models of the supercapacitors in the form of RC ladder networks”, Bulletin of the Polish Academy of Sciences: Technical Sciences 61 (3) (2013) 581–587.