Nonlocal problems for fractional integrodifferential equations via fractional operators and optimal controls

Authors:
JinRong Wang;Yong Zhou;Wei Wei;Honglei Xu
Affiliations:
Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, PR China;Department of Mathematics, Xiangtan University, Xiangtan, Hunan 411105, PR China;Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, PR China;Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, PR China and Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845, Australia
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

This paper investigates nonlocal problems for a class of fractional integrodifferential equations via fractional operators and optimal controls in Banach spaces. By using the fractional calculus, Holder inequality, p-mean continuity and fixed point theorems, some existence results of mild solutions are obtained under the two cases of the semigroup T(t), the nonlinear terms f and h, and the nonlocal item g. Then, the existence conditions of optimal pairs of systems governed by a fractional integrodifferential equation with nonlocal conditions are presented. Finally, an example is given to illustrate the effectiveness of the results obtained.