Advanced Fractional Calculus Approach to RC Electrical Circuit Modeling: Analytical Solutions and Comparative Behavioral Analysis

Abstract

This paper introduces a novel fractional-order model of the classical RC electrical circuit by incorporating the generalized Caputo fractional derivative of order \(0<\psi \le 1\) and a fractional time constant \(\tau _{\psi }\). Using generalized Laplace and inverse Laplace transform techniques, explicit analytical solutions of the proposed model are derived. The study also conducts a comparative analysis between the new fractional RC circuit model and existing models based on classical integer-order derivatives, Caputo, Caputo–Fabrizio, and conformable fractional operators. The results demonstrate that the proposed model offers improved flexibility and accuracy in capturing the memory-dependent dynamics characteristic of real electrical systems. This work contributes to the growing field of fractional calculus applications in electrical engineering by providing a more comprehensive framework for modeling and analysis of RC circuits with non-integer order behavior.