Analytical Contribution to a Cubic Functional Integral Equation with Feedback Control on the Real Half Axis

Synthetic biology involves trying to create new approaches using design-based approaches. A controller is a biological system intended regulate the performance of other processes. The design such controllers can be based on results control theory, including strategies. Integrated feedback central regulation, sensory adaptation, and long-term effects. In this work, we present study cubic functional integral equation with general constraint that may help in investigating some real problems. We discuss existence solutions for an variable class bounded continuous functions BC(R+), by applying technique measure noncompactness R+. Furthermore, establish sufficient conditions dependence state function variable. Finally, remarks discussion are presented demonstrate our results.