RLC electric circuit model of fractional order: a Green's function approach

Abstract

This article uses a hybrid approach that combines Green's function and a fixed point scheme to obtain a semi-analytical solution to the RLC electrical circuit's non-integer order differential equation. The fractional differential equation's order is determined by the two parameters and . The proposed method is unique because it can be extended to general nonlinear fractional systems. Another highly desirable feature of the proposed approach is that the construction of Green's function depends on both endpoints of the time domain, and hence the produced approximate solutions are highly accurate for fractional boundary value problems. We provide examples with figures and tables to demonstrate the effectiveness of our method in solving electrical circuit problems. TThe obtained approximate solutions are compared with exact solutions or numerical simulations to validate the applicability and accuracy of the proposed scheme.