Attractors of Caputo fractional differential equations with triangular vector fields

It is shown that the attractor of an autonomous Caputo fractional differential equation of order alpha is an element of (0, 1) in 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 pich fork bifurcations. The proof uses a result of Cong & Tuan [2] which shows that no two solutions of such a Caputo FDE can intersect in finite time.