Unveiling fractional-order dynamics: A new method for analyzing Rössler Chaos

Abstract

In this manuscript, we investigate the fractional-order Rössler attractor using the Atangana–Baleanu derivative within the metric fixed point theory framework. We establish the existence and uniqueness criteria for the fractional-order Rössler model by employing the $ℱ$-type rational contraction technique through the lens of Atangana–Baleanu in the environment of extended suprametric space. Furthermore, we construct a solid mathematical foundation by applying interpolative Kannan and Reich-Rus-Ćirić type contractions together with specific examples to validate the fixed point results. The two-step Lagrange method performs fractional derivative approximation to study the attractor’s geometric evolution under different parametric conditions. Numerical simulations created new classifications of chaotic behavior that enhance our understanding of fractional dynamics working with chaos theory.