Application of fractional modified taylor wavelets in the dynamical analysis of fractional electrical circuits under generalized caputo fractional derivative

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Abstract This study examines the application of fractional calculus in the analysis and modeling of electrical circuits of fractional order, highlighting its potential to explain the behaviour of complex electrical circuits accurately. In the domain of electrical circuits, fractional differential equations are employed in the analysis and simulation of systems that consist of resistors, capacitors and inductors. In the present paper, a novel approach utilizing fractional order modified Taylor wavelets is implemented to solve the fractional model of RL, LC, RC and RLC electrical circuits under generalized Caputo fractional derivative which offers precise and flexible modeling of non-locality and hereditary characteristics in complex systems. Furthermore, an additional parameter σ (time scale parameter) is incorporated in fractional circuit dynamics to maintain the physical dimensionality. The considered wavelets with the collocation technique offer an efficient solution by converting the fractional model of electrical circuits into a set of algebraic equations which are further solved by using the Newton iteration method. Moreover, this study discusses the significance of Ulam-Hyers stability, emphasizing its role in ensuring stable and reliable circuit performance. The impact of fractional order on the dynamics of the electric circuit model is presented by tables and graphs. The approximate solutions obtained by the proposed method are well comparable with exact solutions and some other existing wavelet-based techniques. The residual errors are also evaluated under various model parameters for fractional orders. Furthermore, the graphs illustrate that the error progressively decreases as the number of wavelets basis increases.