@ARTICLE{10.21494/ISTE.OP.2023.0987,
TITLE={An analysis of the internal nature of fractional order models},
AUTHOR={Jocelyn Sabatier, },
JOURNAL={Entropy: Thermodynamics – Energy – Environment – Economy },
VOLUME={4},
NUMBER={Special issue LILA},
YEAR={2023},
URL={http://openscience.fr/An-analysis-of-the-internal-nature-of-fractional-order-models},
DOI={10.21494/ISTE.OP.2023.0987},
ISSN={2634-1476},
ABSTRACT={Through some mathematical transformations, this paper highlights the internal nature of fractional models described by fractional differential equations or pseudo state space descriptions. In particular, the impulse response computation for considered fractional model using the Cauchy method shows that they exhibit infinitely small and high time constants. The diffusive representation of these models is the deduced. Using Fourier transform a representation of fractional models with a diffusion equation defined on an infinite space domain is then deduced. Fractional models can thus be viewed as doubly infinite dimensional models: a first infinite as they are distributed and a second infinity as they are defined on an infinite domain. This infinite domain or the infinitely large time constants of the impulse response reveal a property intrinsic to fractional models: their infinite memory.}}