Approximate controllability results in α-norm for some partial functional integrodifferential equations with nonlocal initial conditions in Banach spaces

• Autorzy: Ndambomve Patrice , Kpoumie Moussa El-Khalil , Ezzinbi Khalil

Identyfikatory

DOI

10.1515/jaa-2022-2001

• Języki publikacji: EN

Abstrakty

EN

In this work, we discuss the approximate controllability of some nonlinear partial functional integrodifferential equations with nonlocal initial condition in Hilbert spaces.We assume that the corresponding linear part is approximately controllable. The results are obtained by using fractional power theory and α-norm, the measure of noncompactness and theMönch fixed-point theorem, and the theory of analytic resolvent operators for integral equations. As a result, we obtain a generalization of the work of Mahmudov [N. I. Mahmudov, Approximate controllability of evolution systems with nonlocal conditions, Nonlinear Anal. 68 (2008), no. 3, 536-546], without assuming the compactness of the resolvent operator. Our results extend and complement many other important results in the literature. Finally, a concrete example is given to illustrate the application of the main results.

Słowa kluczowe

EN

approximate controllability; integrodifferential equations; nonlocal initial condition; resolvent operator for integral equations; fractional power; measure of noncompactness; Mönch fixed-point theorem

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2023
• Tom: Vol. 29, nr 1
• Strony: 127--142
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Ndambomve Patrice

• Department of Mathematics, Faculty of Science, University of Buea, P.O. Box 63, Buea, South-West Region, Cameroon

• https://orcid.org/0000-0003-2940-1548

autor

Kpoumie Moussa El-Khalil

• Departement de Mathematiques Appliquées et Informatique, Ecole de Géologie et d’Exploitation Minière, Université de Ngaoundéré, B.P. 115 Meiganga, Cameroon

autor

Ezzinbi Khalil

• Département de Mathématiques, Faculté des Sciences Semlalia, Université Cadi Ayyad, B. P. 2390 Marrakech, Morocco

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).