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تسجيل مستخدم جديدAttractors of Caputo fractional differential equations with triangular vector fields
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It is shown that the attractor of an autonomous Caputo fractional differential equation of order $alphain(0,1)$ 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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