Modelling in Fractal analysis is a recent and active research field since 15/20 years. In this period, our group has acquainted an expertise on this topic. Depending on the problem, different tools and techniques are necessary to give a rigorous formulation of classical operators in the Euclidean settings as well as delicate functional inequalities which are instrumental to the study of some BVPs. In view of real world applications it is also crucial to yield a numerical approximation of the solution for the problem at hand. To achieve this goal two steps are necessary. The former is to yield a constructive approach which allows to define an abstract operator in terms of smoother ones, the latter is to construct an efficient numerical approximation scheme. Irregular structures appear in different situations e.g. in problems of wettability [ZLGC], or some problems of human physiology, diffusion of sprays and gases in the lungs [Ku], fractal antennas [WG], tumor growth in biological systems, non-Newtonian fluid mechanics, reaction-diffusion problems, flows through porous media ([D] and references therein), statistical mechanics and quantum fields on fractals [AK1,AK2,AK3]. From the mathematical point of view these problems can be modeled by either scalar or vector linear or nonlinear autonomous or non-autonomous problems possibly with unusual boundary conditions (e.g. Venttsel boundary conditions) involving superposition of operators of different order.
Such problems well describe the impact of a local and a nonlocal diffusion in some concrete situations (e.g. how different types of regional or global restrictions may reduce the spreading of a pandemic disease ).
