Exploring Chaotic Dynamics: A Fractal-Fractional Approach to Financial Modeling and Stability Analysis

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Abstract

Abstract This search uses fractal and fractional derivatives to construct a nancial chaotic model (FCM). The existence and uniqueness of the solution are proved by using the xed point theorem. Using the xed point method, we establish the Ulam-Hyers (UH) stability and Ulam-Hyers-Rassias (UHR) stability for the nonlinear fractal-fractional dierential equations. Numerical solutions are found for FCM using the Adams-Bashforth method (ABM). We tracked the eect of parameters on numerical results, which explained some vague phenomena in the FCM.