Fractional-order modeling of lithium-ion batteries using additive noise assisted modeling and correlative information criterion.

In this paper, the fractional-order modeling of multiple groups of lithium-ion batteries with different states is discussed referring to electrochemical impedance spectroscopy (EIS) analysis and iterative learning identification method. The structure and parameters of the presented fractional-order equivalent circuit model (FO-ECM) are determined by EIS from electrochemical test. Based on the working condition test, a P-type iterative learning algorithm is applied to optimize certain selected model parameters in FO-ECM affected by polarization effect.

Matrix approach to discrete fractional calculus III: non-equidistant grids, variable step length and distributed orders.

In this paper, we further develop Podlubny's matrix approach to discretization of integrals and derivatives of non-integer order. Numerical integration and differentiation on non-equidistant grids is introduced and illustrated by several examples of numerical solution of differential equations with fractional derivatives of constant orders and with distributed-order derivatives. In this paper, for the first time, we present a variable-step-length approach that we call 'the method of large steps', because it is applied in combination with the matrix approach for each 'large step'.

Modelling heat transfer in heterogeneous media using fractional calculus.

This paper presents the results of modelling the heat transfer process in heterogeneous media with the assumption that part of the heat flux is dispersed in the air around the beam. The heat transfer process in a solid material (beam) can be described by an integer order partial differential equation. However, in heterogeneous media, it can be described by a sub- or hyperdiffusion equation which results in a fractional order partial differential equation.

Modulatory influences of ventilatory disorders on electrical stability of the rat heart.

It is a known fact that there is a relationship between some ventilatory disorders and the incidence of ventricular arrhythmias. The aim of our study was to show this relation in the circadian dependence in in-vivo rat models. The electrical stability of the heart was measured by ventricular arrhythmia threshold (VAT) at 3h intervals during a 24h period.