Controllability for fractional evolution inclusions without compactness

Yong  Zhou; V.  Vijayakumar; R.  Murugesu

doi:10.3934/eect.2015.4.507

Article Contents

2015, Volume 4, Issue 4: 507-524. Doi: 10.3934/eect.2015.4.507

This issue Previous Article Stability of nonlinear differential systems with delay Next Article

Controllability for fractional evolution inclusions without compactness

1.
School of Mathematics and Computational Science, Xiangtan University, Hunan 411105
2.
Department of Mathematics, Info Institute of Engineering, Kovilpalayam, Coimbatore - 641 107Tamil Nadu
3.
Department of Mathematics, SRMV College of Arts and Science, Coimbatore - 641 020, Tamil Nadu

Received: July 31, 2015

Revised: September 30, 2015

Published: November 2015

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Abstract

In this paper, we study the existence and controllability for fractional evolution inclusions in Banach spaces. We use a new approach to obtain the existence of mild solutions and controllability results, avoiding hypotheses of compactness on the semigroup generated by the linear part and any conditions on the multivalued nonlinearity expressed in terms of measures of noncompactness. Finally, two examples are given to illustrate our theoretical results.

Keywords:

Mathematics Subject Classification: Primary: 34A08, 34G20, 34G25, 47H10, 47H20, 93B05.

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