Computable Criterions for an Optimal Control of Fractional Integrodifferential Systems in Banach Spaces with Distributed Delays in The Control

Paul Anaetodike Oraekie

In this work,Fractional Integrodifferential Systems in Banach Spaces with  Distributed Delays in the Control of the form is presented for investigation of existence and form of  an optimal control of the  system .Use is made of the Unsymmetric Fubini Theorem to establish the exact  mild solution of the system.The set functions upon which our results hinged are extracted from the mild solution.The concept of the game of pursuit and that of the Signum function are also used to establish results.The main result is built on the maximization of a set function,a technique drawn from the calculus of variation.Necessary and sufficient conditions for existence and form of control for the system are established.