Approximate Controllability of Fractional Delay Dynamic Inclusions with Nonlocal Control Conditions
arXiv:1405.6591 · doi:10.1016/j.amc.2014.05.087
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.
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