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

• Published in: Mathematics (Basel) Vol. 11; no. 5; p. 1133
• Main Authors: El-Sayed, Ahmed M. A., Hashem, Hind H. G., Al-Issa, Shorouk M.
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-03-2023
• Subjects: Analysis; Biological activity; Continuity (mathematics); continuous dependency on a control variable; Control systems design; Control theory; control variable; Darbo’s fixed-point theorem; Feedback control; Feedback control systems; Integral equations; Mathematical analysis; measure of noncompactness; Egypt
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math11051133

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