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

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, 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.