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arXiv · 2108.11715

Attractors of Caputo fractional differential equations with triangular vector fields

Thai Son Doan·Peter E. Kloeden
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Abstract

It is shown that the attractor of an autonomous Caputo fractional differential equation of order $\alpha\in(0,1)$ in $\mathbb{R}^d$ whose vector field has a certain triangular structure and satisfies a smooth condition and dissipativity condition is essentially the same as that of the ordinary differential equation with the same vector field. As an application, we establish several one-parameter bifurcations for scalar fractional differential equations including the saddle-node and the pichfork bifurcations. The proof uses a result of "N. D. Cong and H.T. Tuan, Generation of nonlocal fractional dynamical systems by fractional differential equations. Journal of Integral Equations and Applications, 29 (2017), 1-24" which shows that no two solutions of such a Caputo FDE can intersect in finite time

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Thai Son Doan, Peter E. Kloeden. 2021-08-26. Attractors of Caputo fractional differential equations with triangular vector fields. https://arxiv.org/abs/2108.11715

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