Wang, JinRong; Fečkan, Michal; Zhou, Yong Relaxed controls for nonlinear fractional impulsive evolution equations. (English) Zbl 1263.49038 J. Optim. Theory Appl. 156, No. 1, 13-32 (2013). Summary: In this paper, we study optimal relaxed controls and relaxation of nonlinear fractional impulsive evolution equations. Firstly, the existence of piecewise continuous mild solutions for the original fractional impulsive control system is established. Secondly, a fractional impulsive relaxed control system is constructed by using a regular countably additive measure and convexifying the original control system. Thirdly, optimal relaxed controls and relaxation theorems are obtained. Finally, an application to initial-boundary value problems of fractional impulsive parabolic control systems is considered. Cited in 1 ReviewCited in 36 Documents MSC: 49N25 Impulsive optimal control problems 49J45 Methods involving semicontinuity and convergence; relaxation 34A08 Fractional ordinary differential equations Keywords:fractional impulsive evolution equations; existence; relaxed trajectories; optimal relaxed controls; relaxation PDFBibTeX XMLCite \textit{J. Wang} et al., J. Optim. Theory Appl. 156, No. 1, 13--32 (2013; Zbl 1263.49038) Full Text: DOI References: [1] Baleanu, D., Machado, J.A.T., Luo, A.C.-J.: Fractional Dynamics and Control. Springer, New York (2012) · Zbl 1231.93003 [2] Diethelm, K.: The Analysis of Fractional Differential Equations. Lecture Notes in Mathematics. Springer, New York (2010) · Zbl 1215.34001 [3] Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: In: Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, vol. 204. 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