Modelling and Analysis of Fractional Behaviours: Alternative Approaches and Characterization

Dear Colleagues,

An implicit link exists in the literature between fractional behaviours and fractional differentiation based models. However, fractional behaviours and fractional differentiation based models are two distinct concepts. One designates a property or a particular behaviour of a physical system and the other designates a model class that can capture fractional behaviours.

Fractional behaviours appear in numerous domains (of physical, biological, thermal origin). They often result from stochastic physical phenomena (diffusion, diffusion reaction, adsorption, absorption, aggregation, fragmentation, etc.) that can operate on a fractal space of dimension  and that generate time kinetics (or fractional behaviours) linked to the dimension . Fractional behaviours are ubiquitous, and faced with the drawbacks now associated with the fractional differentiation based models, new modelling tools must be found.

The goal of this Special Issue is to bring out new modelling tools for fractional behaviours (other than usual and strict fractional differentiation or integration based operators), as well as to study their properties and their applications in engineering sciences. Considering fractional behaviours without being limited to fractional models opens up countless avenues of research in the field of model analysis and identification. To avoid unnecessary fractionalizations, this Special Issue also focuses on the methods used to characterize the existence of fractional behaviour in measured data and to theoretical justifications for fractional behaviours. We seek to collect papers that achieve the following aims:

• Discuss and highlight the link between the fractal dimension and fractional behaviours;
• Propose a method that proves that data exhibit fractional behaviour and require specific modelling tools;
• Present alternative modelling tools to fractional calculus-based models for fractional behaviours (for instance, convolution models with non singular kernels, non-linear models, tim- varying models, partial differential equations, peridynamic models …);
• Describe parameter identification methodologies for the above alternative models;
• Present applications of these alternative modelling tools.

Prof. Dr. Jocelyn Sabatier
Guest Editor

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• fractional behaviours
• modelling
• non-singular kernels
• fractal