4.5 Article

A class of fractional evolution equations and optimal controls

期刊

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
卷 12, 期 1, 页码 262-272

出版社

PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2010.06.013

关键词

Fractional evolution equations; Analytic compact semigroup; Fractional power space; alpha-mild solutions; Optimal controls

资金

  1. National Natural Science Foundation of PR China [10971173]
  2. National Natural Science Foundation of Guizhou Province [2142]
  3. Youth Teachers Natural Science Foundation of Guizhou University [083]

向作者/读者索取更多资源

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. (C) 2010 Elsevier Ltd. All rights reserved.

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