Lagrange optimal controls and time optimal controls for composite fractional relaxation systems

Abstract

Abstract By means of the theory of resolvent and Schauder’s fixed point, the existence results of semilinear composite fractional relaxation systems are acquired. Then the new approach of setting up minimizing sequences twice is used to derive the optimal pairs without Lipschitz assumptions on nonlinear functions and nonlocal items. Moreover, the reflexivity of a state space X is not required by making full use of the compact method. Our results essentially improve and generalize those on optimal controls in recent literature.

Keywords

• fractional composite relaxation systems
• resolvent operators
• optimal controls
• time optimal
• mild solution