Applied Mathematics and Optimization, Vol.84, No.3, 3045-3082, 2021
Sensitivity Analysis of Optimal Control Problems Governed by Nonlinear Hilfer Fractional Evolution Inclusions
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 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.