Sobre difusões normal e anômala-formalismos e aplicações - Santos, Maike Antonio Faustino dos (2015)
The diffusion processes has been extensively studied in recent decades through experiments, theory and numerical simulations. In this work, firstly, we emphasized some concepts associated to the origins of the diffusion, which follow several researches started in the XIX century, and also introduced the denifition of anomalous diffusion. Secondly, we studied the development of some formalisms that incorporate the non-Markovian anomalous processes in the diffusion scenario. Finally, we investigated some problems involving anomalous processes and obtained the solutions using the method of Green?s function for a system governed by a Fokker-Planck equation related to the comb model, and for a fractional Schrödinger equation. We also used some ideas from the nonextensive statistical mechanics to investigate a system governed by a nonlinear Fokker-Planck equation.