2014/05/26 by Amar Debbouche, Delfim F. M. Torres · 81 citations
Engineering · Mathematics · #Applied mathematics #Computer science #Control (management) #Control theory (sociology) #Controllability #Differential inclusion #Fixed point #Fixed-point theorem #Fractional Differential Equations Solutions #Fractional calculus #Hilbert space #Mathematical analysis #Mathematics #Nonlinear Differential Equations Analysis #Set (abstract data type) #Stability and Controllability of Differential Equations #math.OC #msc:26A33 #msc:34A60 #msc:34G25 #msc:93B05
paper · pdf · doi:10.1016/j.amc.2014.05.087
published in Applied Mathematics and Computation 243, 161-175 (Elsevier BV) · This is a preprint of a paper whose final and definite form will be published in Applied Mathematics and Computation, ISSN 0096-3003 (see http://www.sciencedirect.com/science/journal/00963003). Submitted 12/Feb/2013; Revised 04/May/2014; Accepted 25/May/2014
arxiv created 2014/05/26 · openalex publication_date 2014/06/20 · arxiv updated 2014/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We introduce a nonlocal control condition and the notion of approximate controllability for fractional order quasilinear control inclusions. Approximate controllability of a fractional control nonlocal delay quasilinear functional differential inclusion in a Hilbert space is studied. The results are obtained by using the fractional power of operators, multi-valued analysis, and Sadovskii's fixed point theorem. Main result gives an appropriate set of sufficient conditions for the considered system to be approximately controllable. As an example, a fractional partial nonlocal control functional differential inclusion is considered.