Fractional calculus is a mathematical approach dealing with derivatives and integrals of arbitrary and complex orders. Therefore, it adds a new dimension to understand and describe basic nature and behavior of complex systems in an improved way. Here we use the fractional calculus for modeling electrical properties of biological systems. We derived a new class of generalized models for electrical impedance and applied them to human skin by experimental data fitting. The primary model introduces new generalizations of: 1) Weyl fractional derivative operator, 2) Cole equation, and 3) Constant Phase Element (CPE). These generalizations were described by the novel equation which presented parameter related to remnant memory and corrected four essential parameters We further generalized single generalized element by introducing specific partial sum of Maclaurin series determined by parameters We defined individual primary model elements and their serial combination models by the appropriate equations and electrical schemes. Cole equation is a special case of our generalized class of models for Previous bioimpedance data analyses of living systems using basic Cole and serial Cole models show significant imprecisions. Our new class of models considerably improves the quality of fitting, evaluated by mean square errors, for bioimpedance data obtained from human skin. Our models with new parameters presented in specific partial sum of Maclaurin series also extend representation, understanding and description of complex systems electrical properties in terms of remnant memory effects.

No abstract

No abstract

The world's perennial need for energy and microelectronic miniaturization brings with it a broad set of technological and scientific challenges. Materials characterized by precise microstructural architectures based on fractal analysis and ranging in size down to nano scale represent an important avenue for finding novel solutions. Deep materials structure hierarchies of this type open new possibilities in capacity according to the Heywang model, especially when extended by a fractals approach and intergranular relationships supported and recognized by their fractal nature. These developments are opening new frontiers in microelectronics miniaturization. They build on early fractal applications that were used as tools in miniaturization research and also provided application perspectives for diverse energy technologies. In other words, fractals, as a crucial concept of modern theoreticalexperimental physics and materials sciences, are tightly linked to higher integration processes and microelectronics miniaturization. They also hold potential for meeting the energy exploitation challenge. In this research context, for the first time we characteristics -for example, fractal dimensions and final properties of nextgeneration fractal microelectronics.

The main goal of our research is to find the connection between micro particles and microorganisms motion in the Nature, considered as Brownian’s Motion within the fractal’s nature. For ceramics and generally material science it is important to clarify the particles motion and other phenomena, especially for grains and pores. Our idea is to establish control over the relation order–disorder on particle motion and their collision effects by Brownian motion phenomena in the frame of fractal nature matter. We performed some experiments and got interesting results based on microorganism motion initiated by different outer energetic impulses. This is practically the idea of biomimetic correlation between particles and microorganisms Worlds, what is very original and leads towards biunivocal different phenomena’s understanding. Another idea is to establish some controlling effects for electro ceramic particle motion in chemical-materials sciences consolidation by some phenomena in the nature. These important research directions open new frontiers with very specific reflections for future of microelectronics materials.