Approximate Controllability of Fractional Delay Dynamic Inclusions with Nonlocal Control Conditions
Abstract
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.
Keywords
Cite
@article{arxiv.1405.6591,
title = {Approximate Controllability of Fractional Delay Dynamic Inclusions with Nonlocal Control Conditions},
author = {Amar Debbouche and Delfim F. M. Torres},
journal= {arXiv preprint arXiv:1405.6591},
year = {2014}
}
Comments
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