An efficient method for the fractional electric circuits based on Fibonacci wavelet

In this article, we provide effective computational algorithms based on Fibonacci wavelet (FW) to approximate the solution of fractional order electrical circuits (ECs). The proposed computational algorithm is novel and has not been previously utilized for solving ECs problems. Firstly, we have constructed the operational matrices of fractional integration (OMFI). Secondly, we transform the given initial value problems into algebraic equations, we used the Riemann–Liouville (R–L) fractional integral operator. The proposed approach is capable of handling a wide range of fractional order dynamics in ECs. To validate the effectiveness of the method, four models of electrical circuits with fractional order parameter are considered. The numerical results are compared with exact solutions and absolute errors are calculated to demonstrate the accuracy and efficiency of the approach. The proposed method provides a valuable tool for analyzing and designing fractional order systems in electrical engineering, offering improved accuracy and capturing the intricate behavior of complex systems. •We proposed a novel technique to study the electric circuit models in the sense of Caputo fractional derivative and Fibonacci wavelet.•We have constructed operational matrices of fractional integration and used it in the subsequent steps to approximate the solutions of models.•The given problems of the fractional order electrical circuits are transformed into algebraic equations using the Riemann–Liouville fractional integral operator.•Graphical representation is shown with simulation to illustrate the effectiveness of the models.