New discussion on global existence and attractivity of mild solutions for nonautonomous integrodifferential equations with state-dependent delay
Diop, M., Ndiaye, A., Fall, M., Traore, M. (2023). New discussion on global existence and attractivity of mild solutions for nonautonomous integrodifferential equations with state-dependent delay. EKB Journal Management System, 11(2), 1-16. doi: 10.21608/ejmaa.2023.298748
Mamadou Abdoul Diop; Abdoul Aziz Ndiaye; Mbarack Fall; Mariama B Traore. "New discussion on global existence and attractivity of mild solutions for nonautonomous integrodifferential equations with state-dependent delay". EKB Journal Management System, 11, 2, 2023, 1-16. doi: 10.21608/ejmaa.2023.298748
Diop, M., Ndiaye, A., Fall, M., Traore, M. (2023). 'New discussion on global existence and attractivity of mild solutions for nonautonomous integrodifferential equations with state-dependent delay', EKB Journal Management System, 11(2), pp. 1-16. doi: 10.21608/ejmaa.2023.298748
Diop, M., Ndiaye, A., Fall, M., Traore, M. New discussion on global existence and attractivity of mild solutions for nonautonomous integrodifferential equations with state-dependent delay. EKB Journal Management System, 2023; 11(2): 1-16. doi: 10.21608/ejmaa.2023.298748

New discussion on global existence and attractivity of mild solutions for nonautonomous integrodifferential equations with state-dependent delay

Electronic Journal of Mathematical Analysis and Applications
Volume 11, Issue 2, July 2023, Page 1-16  XML PDF (442.32 K)
Document Type: Reviews
DOI: 10.21608/ejmaa.2023.298748
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Authors
Mamadou Abdoul Diop email 1; Abdoul Aziz Ndiaye2; Mbarack Fall3; Mariama B Traore4
1Department of Mathematics Gaston Berger University
2Department of Mathematics Gaston Berger University Senegal
3Department of Mathematics Gaston Berger University Senegal
4Department of Mathematics University of Bamako Mali
Abstract
As a result of their adaptability, the functional integrodifferential equations can be utilized in a wide variety of research and engineering subspecialties. In this paper, we study a class of functional integrodifferential equations with state-dependent delay in Banach spaces. We begin by investigating the global existence of mild solutions for this class of functional integrodifferential equations in Banach spaces. These equations have a state-dependent delay. The linear component of these equations is dependent on time and generates a linear evolution system. Using the resolvent operator theory in the sense of Grimmer's fixed point technique, a new set of sufficient conditions is formulated and proven for the global existence of mild solutions for the functional integrodifferential equation with state-dependent delay. In the next part of this investigation, we are going to look into the attractivity of mild solutions for functional integrodifferential equations with state-dependent delay. An example is given in order to illustrate the theory that was obtained. Some well-known results are generalized and extended.
Keywords
Evolution system; Resolvent operator; Infinte delay
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