A novel AA* method for exploring the interplay between fractals, polynomiographs, and fractional calculus

We introduce an innovative numerical approach for estimating fixed points of symmetric generalized nonexpansive mappings within uniformly convex Banach spaces. This approach demonstrates a notably quicker convergence rate relative to existing iterative methods. Its effectiveness is confirmed through comprehensive numerical tests, comprising CPU time comparisons and visual representations created in MATLAB, including polynomiographs. Additionally, using the proposed method, we show that solutions to a type of delay fractional differential equations exist and are unique. Our investigation is performed within the scope of Garcia-Falset type mappings, a wider category that includes nonexpansive and Suzuki mappings, thus broadening the relevance of our method.