title: Boundedness of the solutions for certain classes of fractional differential equations with application to adaptive systems.
abstract: This paper presents the analysis of three classes of fractional differential equations appearing in the field of fractional adaptive systems, for the case when the fractional order is in the interval α ∈(0,1] and the Caputo definition for fractional derivatives is used. The boundedness of the solutions is proved for all three cases, and the convergence to zero of the mean value of one of the variables is also proved. Applications of the obtained results to fractional adaptive schemes in the context of identification and control problems are presented at the end of the paper, including numerical simulations which support the analytical results.
authors.affiliation: Department of Electrical Engineering, University of Chile, Av. Tupper 2007, Santiago de Chile, Chile; Advanced Mining Technology Center, Av. Tupper 2007, Santiago de Chile, Chile. Electronic address: naguila@ing.uchile.cl.
authors.forename: Norelys
authors.initials: N
authors.lastname: Aguila-Camacho
authors.affiliation: Department of Electrical Engineering, University of Chile, Av. Tupper 2007, Santiago de Chile, Chile; Advanced Mining Technology Center, Av. Tupper 2007, Santiago de Chile, Chile. Electronic address: mduartem@ing.uchile.cl.
authors.forename: Manuel A
authors.initials: MA
authors.lastname: Duarte-Mermoud
keywords: Adaptive systems; Error models; Fractional calculus; Fractional differential equations