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The crossover among two or more types of diffusive processes represents avibrant theme in nonequilibrium statistical physics. In this work we proposetwo models to generate crossovers among different L\'evy processes: in thefirst model we change gradually the order of the derivative in the Laplacianterm of the diffusion equation, whereas in the second one we consider acombination of fractional-derivative diffusive terms characterized bycoefficients that change in time.  The proposals are illustrated by considering semi-analytical (i.e.,analytical together with numerical) procedures to follow the time-dependentsolutions. We find changes between two different regimes and it is shown that,far from the crossover regime, both models yield qualitatively similar results,although these changes may occur in different forms for the two models. Themodels introduced herein are expected to be useful for describing crossoversamong distinct diffusive regimes that occur frequently in complex systems.

Monitoring L\'evy-Process Crossovers