A novel Ćirić–Reich–Rus fixed point approach for the existence and uniqueness criterion of a fractional-order Aizawa chaotic system

This manuscript introduces a refined class of functions named as the basic function $F^B$ that erases unnecessary conditions, while maintaining the existence and uniqueness results of fixed points. The desired fixed points results are achieved through an interpolative extended $F^B$-Ćirić–Reich–Rus contraction framework. We prove the validity of our fixed-point results by showing examples that demonstrate these contractions are effective. As an application, we utilized the proposed basic contraction technique to determine the existence and uniqueness criteria for solutions of the fractional-order Aizawa system through the lens of the Atangana–Baleanu fractional derivative. We employed the two-step Lagrange polynomial method as an approximation technique for Atangana–Baleanu derivatives before examining the graphical behavior and Lyapunov exponents of the fractional Aizawa attractor for practical applications.