This study investigates Thomas’ cyclically symmetric attractor dynamics with mathematical and electronic simulations using a proportional fractional derivative to comprehend the dynamics of a given chaotic system. The three-dimensional chaotic flow was examined in detail with Riemann-Liouville derivative for different values of the fractional index to highlight the sensitivity of chaotic systems with initial conditions. Thus, the dynamics of the fractional index system were investigated with Eigenvalues, Kaplan–Yorke dimension, Lyapunov exponent, and NIST testing, and their corresponding trajectories were visualized with phase portraits, 2D density plot, and Poincaré maps. After obtaining the results, we found that the integer index dynamics are more complex than the fractional index dynamics. Furthermore, the chaotic system circuit is simulated with operational amplifiers for different fractional indices to generate analog signals of the symmetric attractor, making it an important aspect of engineering. The qualitative application of our nonlinear chaotic system is then applied to encrypt different data types such as voice, image, and video, to ensure that the developed nonlinear chaotic system can widely applied in the field of cyber security.