This paper investigates several strategies for modeling electrochemical impedance, in particular, exploring the effects of fractional calculus. It focuses on the theoretical approach for describing systems with anomalous diffusion
as a result, these effects can be analytically expressed as functions of frequency when different boundary conditions are considered. Starting with the normal case as a reference scenario, this study discusses how to increase the complexity of mathematical solutions by generalizing fundamental equations. The second strategy extends the continuity equation to include a fractional contribution. Subsequently, Fick's law is also extended, considering a case that incorporates a fractal derivative. Finally, we utilize electrochemical impedance to determine electric conductivity, analyze mean-square displacement, and connect it to the diffusion process.