Abstract 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 artículo 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 teoría desarrollada

Naphthalene biodegradation was studied using the bacterial strain Pseudomonas putida S2. Three medium variables out of seven medium components were selected under Plakett-Burman (PB) design as having significant response on naphthalene biodegradation. These variables were citric acid (additional carbon sources), ammonium sulfate and sodium chloride. The levels of these three variables were optimized by the application of genetic algorithm (GA) based response surface methodology (RSM) in terms of maximum biodegradation efficiency. The maximum biodegradation efficiency of 55.51% was observed at concentrations of 1.0 g L-1, 1.0 g L-1, and 0.7g L-1 for citric acid, ammonium sulfate and sodium chloride, respectively. In addition, the interactive effects of significant medium variables were analyzed using three dimensional surface plots simulated by network output in terms of maximum fitness function.