Monitoring Lévy-process crossovers

Abstract The crossover among two or more types of diffusive processes represents a vibrant theme in nonequilibrium statistical physics. In this work we propose models to generate crossovers different Levy processes: the first model change gradually order derivative Laplacian term diffusion equation, whereas second one consider combination fractional-derivative terms characterized by coefficients that time. proposals are illustrated considering semi-analytical (i.e., analytical together with numerical) procedures follow time-dependent solutions. We find changes between regimes and it is shown that, far from regime, both yield qualitatively similar results, although these may occur forms for models. introduced herein expected be useful describing distinct frequently complex systems.