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Research Article | Open Access

Interpretation on nonlocal neutral functional differential equations with delay

Kottakkaran Sooppy Nisar1( ), Kasilingam Munusamy2, Chokkalingam Ravichandran3, Sriramulu Sabarinathan4
Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia
Department of Mathematics, Hindusthan College of Engineering and Technology, Coimbatore 641032, India
Department of Mathematics, Kongunadu Arts and Science College (Autonomous), Coimbatore 641029, Tamil Nadu, India
Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulthur 603203, Tamil Nadu, India
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Abstract

This work deals with the existence and continuous dependence of an integral solution for neutral integro-differential equations with a nonlocal condition. This result is established by using an integrated resolvent operator under conditions of Lipschitz continuity and uniqueness via the Banach fixed point technique. We also study the existence of a strict solution on reflexive and general Banach spaces. In the last section, an example is provided related to this theory.

Keywords

integro-differential equationsintegrated resolvent operatorLipschitz conditionstrict solutionfixed point theorem
CLC number: 34B10, 35B65, 37L05, 45K05, 47H10, 47N20

References

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AIMS Mathematics
Volume 8 Issue 11,
November 2023
Pages 25611-25632
DOI: 10.3934/math.20231307

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Cite this article:
Nisar KS, Munusamy K, Ravichandran C, et al. Interpretation on nonlocal neutral functional differential equations with delay. AIMS Mathematics, 2023, 8(11): 25611-25632. https://doi.org/10.3934/math.20231307

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Received: 07 May 2023
Revised: 24 July 2023
Accepted: 15 August 2023
Published: 15 November 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)