Two fractional order Langevin equation with new chaotic dynamics

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Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
Volume:72 Issue:3
Two fractional order Langevin equation with new chaotic dynamics

Two fractional order Langevin equation with new chaotic dynamics

Authors : Meriem Mansouria BELHAMITI, Zoubir DAHMANİ, Mehmet Zeki SARIKAYA

Pages : 663-685

Doi:10.31801/cfsuasmas.1126025

View : 28 | Download : 50

Publication Date : 2023-09-30

Article Type : Research Paper

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, AtanganaBaleanu derivative, fixed point theory, three step Adams Bashforth scheme

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