Abstract
This article studies sensitivity properties of optimal control problems that are governed by nonlinear Hilfer fractional evolution inclusions (NHFEIs) in Hilbert spaces, where the initial state \(\xi \) is not the classical Cauchy, but is the Riemann–Liouville integral. First, we obtain the nonemptiness and the compactness properties of mild solution sets \(\mathbb {S}(\xi )\) for NHFEIs, and also establish an extension Filippov’s theorem. Then we obtain the continuity and upper semicontinuity of optimal control problems connected with NHFEIs depending on a initial state \(\xi \) as well as a parameter \(\lambda \). Finally, An illustrating example is given.
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This work was supported by the National Natural Science Foundation of China (11772306,11961014), Foundation of Guilin University of Technology (GUTQDJJ2017062), Guangxi Natural Science Foundation (2018GXNSFAA281021, 2018GXNSFBA281020), Guangxi Science and Technology Base Foundation(AD20159017), and the Fundamental Research Funds for the central Universities, China University of Geosciences (Wuhan) (CUGGC05)
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Jiang, Y., Zhang, Q., Chen, A. et al. Sensitivity Analysis of Optimal Control Problems Governed by Nonlinear Hilfer Fractional Evolution Inclusions. Appl Math Optim 84, 3045–3082 (2021). https://doi.org/10.1007/s00245-020-09739-3
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DOI: https://doi.org/10.1007/s00245-020-09739-3
Keywords
- Nonlinear Hilfer fractional evolution inclusions
- Optimal control problem
- Sensitivity properties
- Mild solutions
- Filippov’s theorem