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Zbl 1228.45015
Wang, Jinrong; Zhou, Yong; Wei, Wei; Xu, Honglei
Nonlocal problems for fractional integrodifferential equations via fractional operators and optimal controls. (English)
[J] Comput. Math. Appl. 62, No. 3, 1427-1441 (2011). ISSN 0898-1221

Summary: We investigate nonlocal problems for a class of fractional integrodifferential equations via fractional operators and optimal controls in Banach spaces. By using the fractional calculus, Hölder 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.

MSC 2000:: *45K05 Integro-partial differential equations
34A08
49J15 Optimal control problems with ODE (existence)

Keywords: nonlocal problems; fractional integrodifferential equations; mild solutions; existence; optimal controls

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