Fractional Electrical Impedances in Botanical Elements

Abstract

Fractional calculus (FC) is no longer considered solely from a mathematical viewpoint, and is now applied in many emerging scientific areas, such as electricity, magnetism, mechanics, fluid dynamics, and medicine. In the field of dynamical systems, significant work has been carried out proving the importance of fractional order mathematical models. This article studies the electrical impedance of vegetables and fruits from a FC perspective. From this line of thought, several experiments are developed for measuring the impedance of botanical elements. The results are analyzed using Bode and polar diagrams, which lead to electrical circuit models revealing fractional-order behaviour.

Application of the multi-step differential transform method to solve a fractional human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells

“…Many mathematicians and applied researchers have tried to model real processes using the fractional calculus. Jesus, Machado and Cunha [17] analyzed the fractional order dynamics in botanical electrical impedances. In biology, it has been deduced that the membranes of cells of biological organism have fractional order electrical conductance [18] and then are classified in groups of non-integer order models.…”

Fast tensor product solvers for optimization problems with fractional differential equations as constraints

“…Fractional calculus is often used due to the inadequateness of traditional schemes to describe certain phenomena, such as anomalous diffusion, anaelasticity [16] and viscoelasticity [44,88]. The applications include electrical circuits [39,73], electro-analytical chemistry [84], biomechanics [27], and image processing [91].…”

A Neural Network Approach for Solving Fractional-Order Model of HIV Infection of CD4+T-Cells

“…Nigmatullin and Nelson described in terms of fractional kinetics in complex systems [10]. Jesus, Machado and Cunha analyzed the fractionalorder dynamics in botanical electrical impedances [5], [6]. Petrovic, Spasic and Atanackovic developed a fractional-order mathematical model of a human root dentin [8].…”