This paper introduces new formulas for generalized Hattaf fractal-fractional operators and presents a novel formulation of Gronwall’s inequality using the generalized Hattaf fractal-fractional integral. The research thoroughly investigates the existence and uniqueness of solutions for nonlinear generalized fractal-fractional differential equations ( \(\mathcal {GFFDE}\) ) by employing the Banach contraction principle. Additionally, the study examines the stability of Ulam Hyers ( \({\mathcal{U}\mathcal{H}}\) ) and Ulam Hyers-Rassias ( \(\mathcal {UHR}\) ) for nonlinear \(\mathcal {GFFDE}\) . The theoretical results are illustrated through an example. To address the computational aspect, a numerical scheme utilizing Lagrange polynomial interpolation is proposed to approximate solutions of \(\mathcal {GFFDE}\) . We also analyze the approximation error associated with the proposed numerical scheme. Finally, we apply our numerical approach when the precise solution is known. By employing this method, we demonstrate the practicality and significance of our research through its application to a generalized fractal-fractional chaotic system. The numerical simulations indicate that the suggested approach is exceptionally effective, precise, and achieves rapid convergence.
