Faced with the limitations and drawbacks of fractional calculus and fractional calculus based models [1], and keeping in mind that that “fractional calculus-based models” and “fractional behaviours” (or power law long memory type behaviours) are two different concepts:
– one denotes a particular class of models and
– the other is a class of dynamical behaviours that can be generated and modelled by a wide variety of mathematical tools other than fractional calculus (thus without limitations and drawbacks associated to fractional models),
I decided to reorient my research to focus on fractional behaviours using any modelling and analysis tools other than fractional calculus-based tools [1].
It turns out that some non-linear models, diffusion equations with spatially variable coefficients, distributed delay models, convolution models with rational kernels, or also peridynamics models are able to generate fractional behaviours and are all useful models to overcome the shortcomings of fractional calculus-based models.
My research topics therefore focuses on the study of these models and the development of identification methods dedicated to these models. It also focuses on understanding the origins of fractional behaviours in order to find other classes of possible models. Comparing these modeling tools with real data is also an important part of my activity.
Considering fractional behaviours without being limited to fractional calculus based models opens up countless avenues of research in the field of analysis, modelling, system identification, control,…
[1] – Talk Video
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