Numerical Investigation of the Fractional Oscillation Equations under the Context of Variable Order Caputo Fractional Derivative via Fractional Order Bernstein Wavelets

This article describes an approximation technique based on fractional order Bernstein wavelets for the numerical simulations of fractional oscillation equations under variable order, and the fractional order Bernstein wavelets are derived by means of fractional Bernstein polynomials. The oscillation equation describes electrical circuits and exhibits a wide range of nonlinear dynamical behaviors. The proposed variable order model is of current interest in a lot of application areas in engineering and applied sciences. The purpose of this study is to analyze the behavior of the fractional force-free and forced oscillation equations under the variable-order fractional operator. The basic idea behind using the approximation technique is that it converts the proposed model into non-linear algebraic equations with the help of collocation nodes for easy computation. Different cases of the proposed model are examined under the selected variable order parameters for the first time in order to show the precision and performance of the mentioned scheme. The dynamic behavior and results are presented via tables and graphs to ensure the validity of the mentioned scheme. Further, the behavior of the obtained solutions for the variable order is also depicted. From the calculated results, it is observed that the mentioned scheme is extremely simple and efficient for examining the behavior of nonlinear random (constant or variable) order fractional models occurring in engineering and science.Comment: This is a preprint of a paper whose final and definite form is published Open Access in 'Mathematics' at [http://dx.doi.org/10.3390/math11112503

Modeling of the Resonant Inverter for Wireless Power Transfer Systems Using the Novel MVLT Method

Wireless power transfer (WPT) is a power transfer technique widely used in many industrial applications, medical applications, and electric vehicles (EVs). This paper deals with the dynamic modeling of the resonant inverter employed in the WPT systems for EVs. To this end, the Generalized State-Space Averaging and the Laplace Phasor Transform techniques have been the flagship methods employed so far. In this paper, the modeling of the resonant inverter is accomplished by using the novel Modulated Variable Laplace Transform (MVLT) method. Firstly, the MVLT technique is discussed in detail, and then it is applied to model a study-case resonant inverter. Finally, a study-case resonant inverter is developed and utilized to validate the theoretical results with MATLAB/Simulink