Optimal Control for a Class of Riemann-Liouville Fractional Evolution Inclusions
- there exists such that
- for every and any ,
- for , the operator is strongly continuous.
- for , if the operator is compact, is a compact operator.
- If is convex (closed) in Z for all , then F is said to be convex (closed)-valued.
- If is relatively compact for every bounded subset D of X, then F is said to be completely continuous.
- If is an open subset of X for every open subset V of Z, then F is said to be upper semi-continuous(u.s.c.) on X.
- If the graph is a closed subset of , then F is said to be closed.
- If there is an element satisfying , then F is said to have a fixed point in X.
- there exists a function such that
- for a.e. , the set is relatively compact in X.
3. Existence of Mild Solutions
- for each , is measurable to t and for every , is u.s.c. to x. For every ,
- There exists a continuous nondecreasing function satisfying and such that
4. Existence of Optimal Control
5. An Application
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Yang, H.; Ren, Q. Optimal Control for a Class of Riemann-Liouville Fractional Evolution Inclusions. Symmetry 2022, 14, 248. https://doi.org/10.3390/sym14020248
Yang H, Ren Q. Optimal Control for a Class of Riemann-Liouville Fractional Evolution Inclusions. Symmetry. 2022; 14(2):248. https://doi.org/10.3390/sym14020248Chicago/Turabian Style
Yang, He, and Qian Ren. 2022. "Optimal Control for a Class of Riemann-Liouville Fractional Evolution Inclusions" Symmetry 14, no. 2: 248. https://doi.org/10.3390/sym14020248