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In recent years, the use of variable-order differential operators has emergedas a powerful tool in the analysis of nonlinear fractional differentialequations and chaotic systems. In finance, the accurate prediction of markettrends and the ability to make informed investment decisions is of greatimportance, and the integration of artificial intelligence and mathematics hasgreatly improved the accuracy of these predictions. In this study, we displayedan analysis of adaptive equations produced by three fractional derivatives: theRiemann-Lioville, Caputo-Fabrizio, and Atangana-Baleanu fractional derivatives.These fractional derivatives were employed to analyze financial models in orderto gain a deeper understanding of the complex dynamics of financial markets.The models studied were the Lorenz system, Rossler system, and Shilnikovcashless model. The results showed that each fractional derivative producedvarying outcomes and computation times, highlighting the importance ofselecting the appropriate mathematical approach and software for financialmodeling. The findings of this study underscore the continued integration ofArtificial Intelligence and mathematics in financial analysis anddecision-making, driving the future of investment strategies and marketpredictions.The application of variable-order differential operators in theanalysis of nonlinear fractional differential equations and chaotic systems isan important and growing area of research that holds great promise for thefield of finance.

Numerically Unveiling Hidden Chaotic Dynamics in Nonlinear Differential  Equations with Riemann-Liouville, Caputo-Fabrizio, and Atangana-Baleanu  Fractional Derivatives