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Approximate Controllability for Fractional Differential Equations of Sobolev Type Via Properties on Resolvent Operators

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Abstract

This paper treats the approximate controllability of fractional differential systems of Sobolev type in Banach spaces. We first characterize the properties on the norm continuity and compactness of some resolvent operators (also called solution operators). And then via the obtained properties on resolvent operators and fixed point technique, we give some approximate controllability results for Sobolev type fractional differential systems in the Caputo and Riemann-Liouville fractional derivatives with order 1 < α < 2, respectively. Particularly, the existence or compactness of an operator E−1 is not necessarily needed in our results.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xidian University, Xi’an, 710071, Shaanxi, China

    Yong-Kui Chang

  2. Instituto de Matemática y Física, Universidad de Talca Casilla, 747, Talca, Chile

    Aldo Pereira & Rodrigo Ponce

Authors
  1. Yong-Kui Chang
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  2. Aldo Pereira
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  3. Rodrigo Ponce
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Correspondence to Yong-Kui Chang.

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Chang, YK., Pereira, A. & Ponce, R. Approximate Controllability for Fractional Differential Equations of Sobolev Type Via Properties on Resolvent Operators. FCAA 20, 963–987 (2017). https://doi.org/10.1515/fca-2017-0050

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  • DOI: https://doi.org/10.1515/fca-2017-0050

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