| Abstract: |
| Aim of this talk is to present some recent results on fractal and fractional problems, that is problems having some non-integer order features. Fractal refers to geometrical structures with non-integer dimension, while fractional is the non-integer order of differential operators.
More precisely, the present talk is concerned with the study of fractional problems arising as models of fractional processes on irregular structures: domains with non-smooth boundaries, fractal boundaries and fractal layers.
Several physical and natural phenomena are characterized on one hand by the presence of different temporal and spatial scales, on the other by the presence of contacts among different components through rough (prefractal and fractal) interfaces.
Our aim is to propose mathematical models to investigate these phenomena from an analytical point of view as well as their numerical approximation. |
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