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Fractional finite time delay evolution systems and optimal controls in infinite-dimensional spaces. (English) Zbl 1241.26005

Summary: This paper concerns the fractional finite time delay evolution systems and optimal control in infinite-dimensional spaces. A suitable mild solution of the fractional finite time delay evolution systems is introduced. Using the singular version of the Gronwall inequality with finite time delay, we obtain some sufficient conditions for the existence, uniqueness and continuous dependence of mild solutions of these control systems. A formulation for the fractional Lagrange problem is introduced. The existence of optimal pairs of fractional-time-delay evolution systems is also presented. Finally, an example is given for demonstration.

MSC:

26A33 Fractional derivatives and integrals
26A42 Integrals of Riemann, Stieltjes and Lebesgue type
39B72 Systems of functional equations and inequalities
47J35 Nonlinear evolution equations
93C23 Control/observation systems governed by functional-differential equations
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