Wavelet methods for fractional electrical circuit equations

Abstract

Classical electric circuits consists of resistors, inductors and capacitors which have irreversible and lossy properties that are not taken into account in classical analysis. FDEs can be interpreted as basic memory operators and are generally used to model the lossy properties or defects. Therefore, employing fractional differential terms in electric circuit equations provides accurate modelling of those circuit elements. In this paper, the numerical solutions of fractional LC, RC and RLC circuit equations are considered to better model those imperfections. To this end, the operational matrices for Bernoulli and Chebyshev wavelets are used to obtain the numerical solutions of those fractional circuit equations. Chebyshev wavelets are orthogonal, and under some circumstances, Bernoulli wavelets can be orthogonal. The wavelet methods' quick convergence and minimal processing load depend on the orthogonality principle. In the proposed method, those FDEs are transformed into algebraic equation systems using operational matrices employing the discrete Wavelets. The performance of those two wavelet methods are compared and contrasted for computational load, speed, and absolute error values. The paper exploits discrete Bernoulli and Chebyshev wavelets for the numerical solution of fractional LC, RC and RLC circuit equations. The fast convergence, low processing burden, and compactness of the Bernoulli and Chebyshev wavelet methods for fractional circuit equation solutions represent the novel contributions of this paper. Numerical solutions and comparisons are also presented to validate the method.