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摘要
This paper concerns the existence of mild solutions for semilinear fractional evolution equations and optimal controls in the a-norm. A suitable alpha-mild solution of the semilinear fractional evolution equations is introduced. The existence and uniqueness of alpha-mild solutions are proved by means of fractional calculus, singular version Gronwall inequality and Leray-Schauder fixed point theorem. The existence of optimal pairs of system governed by fractional evolution equations is also presented. Finally, an example is given for demonstration.
