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.

arXiv commentThis 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

References in corpus (3)

• Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics
• Modified Optimal Energy and Initial Memory of Fractional Continuous-Time Linear Systems
• Approximate Controllability of Fractional Nonlocal Delay Semilinear Systems in Hilbert Spaces

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• Regional Enlarged Observability of Fractional Differential Equations with Riemann-Liouville Time Derivatives
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• A survey on sufficient optimality conditions for delayed optimal control problems