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

Ahmed M. A. El-Sayed (), Hind H. G. Hashem and Shorouk M. Al-Issa
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Ahmed M. A. El-Sayed: Faculty of Science, Alexandria University, Alexandria 21544, Egypt
Hind H. G. Hashem: Faculty of Science, Alexandria University, Alexandria 21544, Egypt
Shorouk M. Al-Issa: Faculty of Arts and Sciences, Department of Mathematics, The International University of Beirut, Beirut 1107, Lebanon

Mathematics, 2023, vol. 11, issue 5, 1-18

Abstract: 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.

Keywords: measure of noncompactness; Darbo’s fixed-point theorem; control variable; continuous dependency on a control variable (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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