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Existence and Approximate Controllability of Fractional Evolution Equations with Nonlocal Conditions Via Resolvent Operators

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Abstract

In this article, we are concerned with the existence of mild solutions as well as approximate controllability for a class of fractional evolution equations with nonlocal conditions in Banach spaces. Sufficient conditions of existence of mild solutions and approximate controllability for the desired problem are presented by introducing a new Green’s function and constructing a control function involving Gramian controllability operator. The discussions are based on Schauder’s fixed point theorem as well as the theory of α-order solution operator and α-order resolvent operator. An example is given to illustrate the feasibility of our theoretical results.

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Authors and Affiliations

  1. Department of Mathematics, Northwest Normal University, Lanzhou, 730070, People’s Republic of China

    Pengyu Chen, Xuping Zhang & Yongxiang Li

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  1. Pengyu Chen
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  2. Xuping Zhang
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  3. Yongxiang Li
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Correspondence to Pengyu Chen.

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Chen, P., Zhang, X. & Li, Y. Existence and Approximate Controllability of Fractional Evolution Equations with Nonlocal Conditions Via Resolvent Operators. Fract Calc Appl Anal 23, 268–291 (2020). https://doi.org/10.1515/fca-2020-0011

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  • DOI: https://doi.org/10.1515/fca-2020-0011

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