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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.

45K05 Integro-partial differential equations
34A08 Fractional ordinary differential equations
49J15 Existence theories for optimal control problems involving ordinary differential equations
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