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Relaxed Controls for Nonlinear Fractional Impulsive Evolution Equations |
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| Authors: | JinRong Wang Michal Fec̆kan Yong Zhou |
| Institution: | 1. Department of Mathematics, Guizhou University, Guiyang, Guizhou, 550025, P.R. China 2. Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, 842 48, Slovakia 3. Mathematical Institute, Slovak Academy of Sciences, ?tefánikova 49, Bratislava, 814 73, Slovakia 4. Department of Mathematics, Xiangtan University, Xiangtan, Hunan, 411105, P.R. China |
| Abstract: | In this paper, we study optimal relaxed controls and relaxation of nonlinear fractional impulsive evolution equations. Firstly, existence of piecewise continuous mild solutions for the original fractional impulsive control system is presented. Secondly, fractional impulsive relaxed control system is constructed by using a regular countably additive measure and making the original control system convexified. Thirdly, optimal relaxed controls and relaxation theorems are obtained. Finally, application to initial-boundary value problem of fractional impulsive parabolic control system is considered. |
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