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

Abstract

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.

Keywords

• Fractional calculus
• Caputo fractional derivatives
• Fibonacci wavelets
• Numerical methods
• Electrical circuits