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 α ∈ ( 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 pichfork 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.