Modelica library for simulating fractional differential equations.

This library contains approximation models for simulating fractional differential operators (for example half-differentiators, i.e., s^0.5). These are used in several physical domains like electrochemistry, viscoelasticity, or heat transfer. An exact representation would use infinite memory, therefore only approximations are used, that cover a certain frequency interval.

The library contains the following elements:

• a block model to approximate the transient behavior of fractional differential operators, using Oustaloup's method
• block models to approximate the transient behavior of fractional differential operators, using Xue's and Carlson's method (discouraged)
• test cases
• examples for applications

Main features of the elements provided are:

• user-defined trade-off between accuracy and simulation speed, by selecting an appropriate approximation order and fitting frequency interval
• good rejection of rounding errors, using a series of first-order elements to approximate the fractional differential operator

Potential applications of the provided elements are:

• modelling the relationship between heat transfer and temperature at the border of a semi-infinite domain
• simulating the transient response of a viscoelastic block, subjected to tension
• tuning fractional PID controllers

The original version of this library was released before the Modelica conference 2015 in Versailles:

Download FractionalOrder (2015-07-28)

This Modelica package is free software and the use is completely at your own risk; it can be redistributed and/or modified under the terms of the Modelica License 2.

Copyright (C) 2015, DLR German Aerospace Center

The library is developed by:

• Alexander Pollok
• Dirk Zimmer

from the German Aerospace Center (DLR) and

• Francesco Casella

from the Politecnico di Milano.

You may report any issues with using the Issues button.

Contributions in the form of Pull Requests are always welcome.