Two fractional order Langevin equation with new chaotic dynamics

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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