A fractional-order 4D chaotic electronic circuit based on the Caputo–Fabrizio derivative: modeling, theoretical analysis and numerical simulation

Purpose This paper introduces a novel four-dimensional chaotic electronic circuit modeled using the Caputo–Fabrizio (CF) Fractional derivative (FD), which features a non-singular, exponentially decaying kernel. The existence, uniqueness, and stability of the system’s solutions are rigorously established through Picard approximation, Banach’s fixed point theorem, and an iterative Laplace transform (LT) technique. A customized fractional Euler method is developed to perform numerical simulations, revealing rich dynamical behavior that depends sensitively on the fractional order a ? (0, 1). The results demonstrate that the proposed fractional-order model effectively captures memory effects, offering a more realistic framework for analyzing complex nonlinear electronic systems compared to classical integer-order approaches. Design/methodology/approach The study introduces a novel four-dimensional chaotic electronic circuit model using the CF FD, which features a non-singular, exponentially decaying kernel. The authors employ Picard approximation and Banach’s fixed point theorem to rigorously establish the existence, uniqueness, and stability of the system’s solutions. An iterative scheme based on the LT is applied to analyze stability, while a customized fractional Euler method is developed for numerical simulations. This approach enables the exploration of the system’s dynamic behavior under varying fractional orders (0 < a = 1), demonstrating how memory effects influence chaos in electronic circuits and offering a more realistic modeling framework compared to classical integer-order systems. Findings The most significant findings of this study revolve around the successful development and analysis of a novel four-dimensional chaotic electronic circuit modeled using the CF FD, which features a non-singular, exponentially decaying kernel. The authors rigorously proved the existence, uniqueness, and stability of the system’s solutions using Picard approximation, Banach’s fixed point theorem, and an iterative LT technique. A customized fractional Euler method was introduced for numerical simulations, revealing that the system exhibits rich chaotic dynamics highly sensitive to the fractional order a (0 < a = 1). These results demonstrate that fractional-order modeling with the CF operator captures memory effects more realistically than classical integer-order models, offering enhanced fidelity in representing real-world electronic systems with inherent memory dependence. Originality/value This work is original in proposing the first four-dimensional chaotic electronic circuit modeled with the CF FD—characterized by a non-singular, exponentially decaying kernel–offering a more physically realistic representation of memory effects than classical fractional models. Its value lies in the rigorous theoretical analysis (existence, uniqueness, and stability via Picard approximation and Banach’s fixed point theorem), the development of a tailored fractional Euler method for simulation, and the demonstration that system dynamics are highly sensitive to the fractional order. These contributions advance both fractional calculus theory and its application in secure communications, circuit design, and chaos-based engineering.