Dynamical properties of a meminductor chaotic system with fractal–fractional power law operator

Abstract

Purpose:This study aims to explore the intricate and concealed chaotic structures of meminductor systems and their applications in applied sciences by utilizing fractal fractional operators (FFOs). Methods:The dynamical analysis of a three-dimensional meminductor system with FFO in the Caputo sense is presented, and a unique solution for the system is obtained via a novel contraction in an orbitally complete metric space. Numerical results are derived using a newly developed method based on Newton polynomial. The analysis includes variations in fractional order and fractal dimension, with a presentation of properties such as Lyapunov spectra, bifurcations, Poincar’e sections, attractor projection, inversion property, and time series analysis. Results:The numerical simulations uncovered intricate hidden attractors for certain values of fractional and fractal orders. This study provides insight into the effects of FFOs on analyzing hidden chaotic attractors and presents a novel approach to understanding and analyzing the dynamics of meminductor systems. The study’s findings contribute to the understanding of the complex and hidden structures of meminductor systems using FFOs. The novel method developed in this study could be applied to other dynamical systems, leading to further advancements in the analysis of complex systems.