On the analytical modeling of fractal memelement and inverse memelement

Abstract

SummaryIn this work, an improved analytical model of fractal memelement in which the pinched point shifting has been considered and the original analytical model of fractal inverse memelement have been proposed. These fractal circuit elements are the memelement, and inverse memelement operates based on the principle of electromagnetic in fractal time/space, which must be applied whenever the current flows through fractal media. These models are important because these memory elements can be realized based on the porous material, which is a fractal media. In addition, they can employ self‐similarity, which is hard to be simulated by using the traditional models. This is because such self‐similarity can be well explained by the fractal set‐based model, yet those traditional models are based on the set of real values. Therefore, for deriving the proposed models, the fractal calculus, which is oriented to the fractal set, has been adopted as the mathematical basis. From the analytical and numerical analyses based on the derived models, it has been found that both memelement and inverse memelement can retain their unique frequency characteristics despite being operated based on the abovementioned principle. In addition, their input–output relationships are mathematically differentiable albeit the inputs and outputs themselves are not.