Two fractional order Langevin equation with new chaotic dynamics

Year 2023, Volume: 72 Issue: 3, 663 - 685, 30.09.2023

Meriem Mansouria Belhamıtı , Zoubir Dahmani , Mehmet Zeki Sarıkaya

https://doi.org/10.31801/cfsuasmas.1126025

Abstract

In 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 theorem under a weak topology, and an illustrative example is then given. Furthermore, 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.

Keywords

Caputo, Caputo-Fabrizio derivative, Atangana–Baleanu derivative, fixed-point theory, three-step Adams-Bashforth scheme

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