Journal
DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS
Volume 11, Issue 1, Pages 71-87Publisher
INT PRESS BOSTON, INC
DOI: 10.4310/DPDE.2014.v11.n1.a4
Keywords
Sobolev type fractional evolution systems; propagation family; measure of noncompactness; mild solutions; controllability
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Funding
- National Natural Science Foundation of China [11201091, 11271309]
- Key Project on the Reforms of Teaching Contents and Course System of Guizhou Normal College
- Doctor Project of Guizhou Normal College [13BS010]
- Specialized Research Fund for the Doctoral Program of Higher Education [20114301110001]
- Key Projects of Hunan Provincial Natural Science Foundation of China [12JJ2001]
- [VEGA-MS 1/0507/11]
- [VEGA-SAV 2/7140/27]
- [APVV-0134-10]
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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.
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