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Nonlocal problems for fractional integrodifferential equations via fractional operators and optimal controls. (English) Zbl 1228.45015
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:
 45K05 Integro-partial differential equations 34A08 Fractional differential equations 49J15 Optimal control problems with ODE (existence)
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