Chaotic and Quasi-Periodic Behaviors in Ferromagnetic Materials: A Dynamical Analysis Utilizing the Truncated Mittag-Leffler Function

This study conducts a thorough analysis of the nonlinear fractional complex Heisenberg ferromagnetic-type Akbota (FCHFA) model to clarify its dynamic behavior. Through rigorous bifurcation analysis, we identify stability transitions and determine critical parameter thresholds, revealing the system’s sensitivity to perturbations. Employing advanced nonlinear dynamics techniques, we explore the fundamental mechanisms governing magnetization evolution. By integrating numerical simulations with analytical methods, we critically evaluate the role of fractional calculus in modeling long-range interactions and temporal memory effects in ferromagnetic systems. The FCHFA model, which incorporates nonlinear spin-wave phenomena and phase transitions, offers a robust framework for analyzing magnetization dynamics. Numerically validated solutions confirm the effectiveness of our methodology, providing new insights into phase transitions and nonlinear wave phenomena. Our findings highlight the crucial role of fractional derivatives in capturing complex magnetization behaviors, thereby enhancing theoretical understanding and broadening the applicability of fractional models in condensed matter physics. This work integrates fractional calculus with ferromagnetic theory, establishing a mathematically rigorous foundation for modeling systems with memory and nonlocal interactions. By rigorously validating numerical and analytical approaches, the study sets a precedent for investigating critical phenomena in fractional-order systems, with significant implications for device design in spintronics and magnetic materials. Furthermore, it demonstrates how fractional derivatives can effectively encapsulate the intricate dynamics of magnetization, including the interplay between memory effects and nonlinearity. By bridging theoretical developments with practical applications, this research not only advances the mathematical framework for studying complex magnetic materials but also opens avenues for innovative technological applications in the field of condensed matter physics.