Fractional calculus in solid mechanics:local versus non-local approach

Several enriched continuum mechanics theories have been proposed by the scientificcommunity in order to develop models capable of describing microstructural effects. The aimof the present paper is to revisit and compare two of these models, whose commondenominator is the use of fractional calculus operators. The former was proposed toinvestigate damage in materials exhibiting a fractal-like microstructure. It makes use of thelocal fractional derivative, which turns out to be a powerful tool to describe irregular patternssuch as strain localization in heterogeneous materials. On the other hand, the latter is anon-local approach that models long-range interactions between particles by means of the Marchaud fractional derivative. Analogies and differences between the two models areoutlined and discussed.