Two fractional order Langevin equation with new chaotic dynamics

Meriem Mansouria BELHAMITI, Zoubir DAHMANİ, Mehmet Zeki SARIKAYA
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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.
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具有新混沌动力学的两分数阶朗之万方程
本文利用Atangana-Baleanu和Caputo-Fabrizio的导数,引入了一类二阶非线性分数阶序朗之万方程。利用弱拓扑下的不动点定理证明了该问题解的存在性,并给出了一个实例。此外,我们提出了Atangana-Baleanu和Caputo导数的Adams-Bashforth三步法的分数阶新版本。通过数值模拟实现了新的非线性混沌动力学。
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