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This paper deals with fractional optimal control for a class of semilinear stochastic equation in Hilbert space setting. To ensure the existence and uniqueness of mild solution, a set of sufficient conditions is constructed. The existence of fractional optimal control for semilinear stochastic system is also discussed. Finally, an example is included to show the applications of the developed theory. RESUMEN Este art́ıculo estudia el control óptimo fraccional para una clase de ecuaciones estocásticas semilineales en un contexto de espacios de Hilbert. Para asegurar la existencia y la unicidad de soluciones blandas, construimos un conjunto de condiciones suficientes. La existencia del control óptimo fraccional para sistemas estocásticos semilineales también es discutido. Finalmente, incluimos un ejemplo para mostrar la aplicabilidad de la teoŕıa desarrollada.

The Solvability and Fractional Optimal Control for Semilinear Stochastic Systems