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, pp-mean continuity and fixed point theorems, some existence results of mild solutions are obtained under the two cases of the semigroup T(t)T(t), the nonlinear terms ff and hh, and the nonlocal item gg. 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.