Optimal control of nonlocal fractional evolution equations in the α-norm of order ( 1 , 2 ) $(1,2)$
Abstract This paper investigates the optimal control for a class of nonlocal fractional evolution equations of order γ ∈ ( 1 , 2 ) $\gamma \in (1,2)$ in Banach spaces. An adequate definition of α-mild solutions is obtained and the existence, uniqueness and continuous dependence of α-mild solutions f...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2021-02-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-021-03312-0 |
| Summary: | Abstract This paper investigates the optimal control for a class of nonlocal fractional evolution equations of order γ ∈ ( 1 , 2 ) $\gamma \in (1,2)$ in Banach spaces. An adequate definition of α-mild solutions is obtained and the existence, uniqueness and continuous dependence of α-mild solutions for the presented control system are also established. The existence of optimal pairs of nonlocal fractional evolution systems is also demonstrated with a view on the construction of the Lagrange problem. Finally, an example is propounded for the presentation of optimal control. |
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| ISSN: | 1687-1847 |