Existence and Approximate Controllability of Fractional Evolution Equations with Nonlocal Conditions Via Resolvent Operators
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...
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| Published in | Fractional calculus & applied analysis Vol. 23; no. 1; pp. 268 - 291 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Warsaw
Versita
01.02.2020
De Gruyter Nature Publishing Group |
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| Online Access | Get full text |
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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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| AbstractList | 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. 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. 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 -order solution operator and -order resolvent operator. An example is given to illustrate the feasibility of our theoretical results. |
| Author | Li, Yongxiang Chen, Pengyu Zhang, Xuping |
| Author_xml | – sequence: 1 givenname: Pengyu surname: Chen fullname: Chen, Pengyu email: chpengyu123@163.com organization: Department of Mathematics, Northwest Normal University – sequence: 2 givenname: Xuping surname: Zhang fullname: Zhang, Xuping organization: Department of Mathematics, Northwest Normal University – sequence: 3 givenname: Yongxiang surname: Li fullname: Li, Yongxiang organization: Department of Mathematics, Northwest Normal University |
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| Keywords | fractional evolution equations approximate controllability order solution operator Primary 26A33 Secondary 34K37, 35R11, 93B05 order resolvent operator nonlocal conditions |
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| SubjectTerms | 35R11 93B05 Abstract Harmonic Analysis Analysis approximate controllability Banach spaces Controllability Evolution Fixed points (mathematics) fractional evolution equations Functional Analysis Integral Transforms Mathematical analysis Mathematics nonlocal conditions Operational Calculus order resolvent operator order solution operator Primary 26A33 Research Paper Secondary 34K37 Stability |
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| Title | Existence and Approximate Controllability of Fractional Evolution Equations with Nonlocal Conditions Via Resolvent Operators |
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