Approximate Controllability and Existence of Mild Solutions for Riemann-Liouville Fractional Stochastic Evolution Equations with Nonlocal Conditions of Order 1 < α < 2
In this paper, we consider the existence of mild solutions and approximate controllability for Riemann-Liouville fractional stochastic evolution equations with nonlocal conditions of order 1 < α < 2. As far as we know, there are few articles investigating on this issue. Firstly, the mild solut...
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| Published in | Fractional calculus & applied analysis Vol. 22; no. 4; pp. 1086 - 1112 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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01.08.2019
De Gruyter Nature Publishing Group |
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| Abstract | In this paper, we consider the existence of mild solutions and approximate controllability for Riemann-Liouville fractional stochastic evolution equations with nonlocal conditions of order 1 <
α
< 2. As far as we know, there are few articles investigating on this issue. Firstly, the mild solutions to the equations are proved using Laplace transform of the Riemann-Liouville derivative. Moreover, the estimations of resolve operators involving the Riemann-Liouville fractional derivative of order 1 <
α
< 2 are given. Then, the existence results are obtained via the noncompact measurement strategy and the Mönch fixed point theorem. The approximate controllability of this nonlinear Riemann-Liouville fractional nonlocal stochastic systems of order 1 <
α
< 2 is concerned under the assumption that the associated linear system is approximately controllable. Finally, the approximate controllability results are obtained by using Lebesgue dominated convergence theorem. |
|---|---|
| AbstractList | In this paper, we consider the existence of mild solutions and approximate controllability for Riemann-Liouville fractional stochastic evolution equations with nonlocal conditions of order 1 <
< 2. As far as we know, there are few articles investigating on this issue. Firstly, the mild solutions to the equations are proved using Laplace transform of the Riemann-Liouville derivative. Moreover, the estimations of resolve operators involving the Riemann-Liouville fractional derivative of order 1 <
< 2 are given. Then, the existence results are obtained via the noncompact measurement strategy and the Mönch fixed point theorem. The approximate controllability of this nonlinear Riemann-Liouville fractional nonlocal stochastic systems of order 1 <
< 2 is concerned under the assumption that the associated linear system is approximately controllable. Finally, the approximate controllability results are obtained by using Lebesgue dominated convergence theorem. In this paper, we consider the existence of mild solutions and approximate controllability for Riemann-Liouville fractional stochastic evolution equations with nonlocal conditions of order 1 < α < 2. As far as we know, there are few articles investigating on this issue. Firstly, the mild solutions to the equations are proved using Laplace transform of the Riemann-Liouville derivative. Moreover, the estimations of resolve operators involving the Riemann-Liouville fractional derivative of order 1 < α < 2 are given. Then, the existence results are obtained via the noncompact measurement strategy and the Mönch fixed point theorem. The approximate controllability of this nonlinear Riemann-Liouville fractional nonlocal stochastic systems of order 1 < α < 2 is concerned under the assumption that the associated linear system is approximately controllable. Finally, the approximate controllability results are obtained by using Lebesgue dominated convergence theorem. In this paper, we consider the existence of mild solutions and approximate controllability for Riemann-Liouville fractional stochastic evolution equations with nonlocal conditions of order 1 < α < 2. As far as we know, there are few articles investigating on this issue. Firstly, the mild solutions to the equations are proved using Laplace transform of the Riemann-Liouville derivative. Moreover, the estimations of resolve operators involving the Riemann-Liouville fractional derivative of order 1 < α < 2 are given. Then, the existence results are obtained via the noncompact measurement strategy and the Mönch fixed point theorem. The approximate controllability of this nonlinear Riemann-Liouville fractional nonlocal stochastic systems of order 1 < α < 2 is concerned under the assumption that the associated linear system is approximately controllable. Finally, the approximate controllability results are obtained by using Lebesgue dominated convergence theorem. |
| Author | Shu, Xiao-Bao Mao, Jianzhong Shu, Linxin |
| Author_xml | – sequence: 1 givenname: Linxin surname: Shu fullname: Shu, Linxin email: shulinxin2066@126.com organization: Institute of Mathematics and Econometrics, Hunan University – sequence: 2 givenname: Xiao-Bao surname: Shu fullname: Shu, Xiao-Bao organization: Institute of Mathematics and Econometrics, Hunan University – sequence: 3 givenname: Jianzhong surname: Mao fullname: Mao, Jianzhong organization: Institute of Mechanical Engineering, Hunan University |
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| SubjectTerms | 26A33 35R60 47J35 Abstract Harmonic Analysis Analysis approximate controllability Controllability Evolution Fixed points (mathematics) Functional Analysis Integral Transforms Mathematical analysis Mathematics mild solutions Mönch fixed point theorem noncompact measurement Nonlinear control Operational Calculus Operators (mathematics) Primary 93B05 Research Paper Riemann-Liouville fractional evolution equations Secondary 34A08 sectorial operators Stochastic systems Theorems |
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| Title | Approximate Controllability and Existence of Mild Solutions for Riemann-Liouville Fractional Stochastic Evolution Equations with Nonlocal Conditions of Order 1 < α < 2 |
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