Dynamics of Partial Differential Equations

Volume 11 (2014)

Number 1

Controllability of Sobolev type fractional evolution systems

Pages: 71 – 87

DOI: https://dx.doi.org/10.4310/DPDE.2014.v11.n1.a4

Authors

Jinrong Wang (School of Mathematics and Computer Science, Guizhou Normal College, Guiyang, Guizho, China)

Michal Feckan (Department of Mathematical Analysis and Numerical Mathematics, Comenius University, Mlynská dolina, Bratislava, Slovakia; and Mathematical Institute, Slovak Academy of Sciences, Štefánikova, Bratislava, Slovakia)

Yong Zhou (Department of Mathematics, Xiangtan University, Xiangtan, Hunan, China)

Abstract

The main purpose of this paper is to investigate a class of Sobolev type semilinear fractional evolution systems in a separable Banach space. Applying a suitable fixed point theorem as well as condensing mapping, controllability results for two class of control sets are established by means of the theory of propagation family and technique of measure of noncompactness. An application involving a partial differential equation with a Caupto fractional derivative is considered.

Keywords

Sobolev type fractional evolution systems, propagation family, measure of noncompactness, mild solutions, controllability

2010 Mathematics Subject Classification

47J35, 93B05, 93C25

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Published 8 April 2014