Abstract
In this paper, we will examine the facts in the image of infinite time delay on the mild solution’s solvability and fractional integro-differential Evolution Equation of Banach space’s optimal control choosing order ? ? (1,2). For investigation of mild solution of the system, continuation, uniqueness and the existence of the solution with the help of grown-wall inequality will be discussed shortly. After constructing the lagrange problem, the demonstration of actuality of optimal control of fractional integro delay system is being proceed. And at the end we will discuss the regarding result by an adequate example.
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