Attractors of Caputo fractional differential equations with triangular vector fields

2021/08/26 by Doan, Thai Son, Kloeden, Peter E.
#34K05 #34K12 #34K16 #34K18 #34K25 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2108.11715

Abstract

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 "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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