Belhamiti, Meriem MansouriaDahmani, ZoubirSarikaya, Mehmet Zeki2024-08-232024-08-2320231303-5991https://doi.org/10.31801/cfsuasmas.1126025https://search.trdizin.gov.tr/tr/yayin/detay/1199612https://hdl.handle.net/20.500.12684/13849In the present paper, we introduce a two-order nonlinear fractional sequential Langevin equation using the derivatives of Atangana-Baleanu and Caputo-Fabrizio. The existence of solutions is proven using a fixed point theo-rem under a weak topology, and an illustrative example is then given. Further-more, we present new fractional versions of the Adams-Bashforth three-step approach for the Atangana-Baleanu and Caputo derivatives. New nonlinear chaotic dynamics are performed by numerical simulations.en10.31801/cfsuasmas.1126025info:eu-repo/semantics/openAccessCaputoCaputo-Fabrizio derivativeAtangana-Baleanu derivativefixed-point theorythree-step Adams-Bashforth schemeArticle7236636851199612WOS:001108742100019Q2