Time optimal controls for Hilfer fractional nonlocal evolution systems without compactness and Lipschitz condition

Abstract

We explore the time optimal control problem for a Hilfer type fractional diffusion nonlocal control system. For this strategy, with the help of the established subordination principle and approximation theory, the abstract model adapted from the addressed diffusion system is tackled by the approximation solvability approach and the resolvent technique. We drop the compactness on semigroup and the Lipschitz restriction on the nonlinear term. We then employ a joint combination of the approach of formulating minimizing approximation sequences twice and the weak topology method to seek suitable trajectory-control dyads. Finally, the time optimal control problem for the diffusion system is solved by exploiting our mentioned abstract results.