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Controllability of Fractional Functional Evolution Equations of Sobolev Type via Characteristic Solution Operators

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Abstract

The paper is concerned with the controllability of fractional functional evolution equations of Sobolev type in Banach spaces. With the help of two new characteristic solution operators and their properties, such as boundedness and compactness, we present the controllability results corresponding to two admissible control sets via the well-known Schauder fixed point theorem. Finally, an example is given to illustrate our theoretical results.

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Acknowledgements

The authors thank the referees for their careful reading of the manuscript and insightful comments. We also acknowledge the valuable comments and suggestions from the editors. Finally, The first author acknowledges the support by Grants VEGA-MS 1/0507/11, VEGA-SAV 2/0124/12 and APVV-0414-07; the second author acknowledges the support by National Natural Science Foundation of China (11201091) and Key Projects of Science and Technology Research in the Chinese Ministry of Education (211169) and the third author acknowledges the support by National Natural Science Foundation of China (11271309), Specialized Research Fund for the Doctoral Program of Higher Education (20114301110001) and Key Projects of Hunan Provincial Natural Science Foundation of China (12JJ2001).

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Authors and Affiliations

  1. Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, 842 48, Bratislava, Slovakia

    Michal Fec̆kan

  2. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Michal Fec̆kan

  3. Department of Mathematics, Guizhou University, Guiyang, Guizhou, 550025, P.R. China

    JinRong Wang

  4. Department of Mathematics, Xiangtan University, Xiangtan, Hunan, 411105, P.R. China

    Yong Zhou

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  1. Michal Fec̆kan
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  2. JinRong Wang
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  3. Yong Zhou
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Correspondence to JinRong Wang.

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Fec̆kan, M., Wang, J. & Zhou, Y. Controllability of Fractional Functional Evolution Equations of Sobolev Type via Characteristic Solution Operators. J Optim Theory Appl 156, 79–95 (2013). https://doi.org/10.1007/s10957-012-0174-7

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  • DOI: https://doi.org/10.1007/s10957-012-0174-7

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