Interpretation on nonlocal neutral functional differential equations with delay

Kottakkaran Sooppy Nisar; Kasilingam Munusamy; Chokkalingam Ravichandran; Sriramulu Sabarinathan; Kottakkaran Sooppy Nisar; Kasilingam Munusamy; Chokkalingam Ravichandran; Sriramulu Sabarinathan

doi:10.3934/math.20231307

AIMS Mathematics

2023, Volume 8, Issue 11: 25611-25632. doi: 10.3934/math.20231307

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Research article

Interpretation on nonlocal neutral functional differential equations with delay

1.
Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia
2.
Department of Mathematics, Hindusthan College of Engineering and Technology, Coimbatore 641032, India
3.
Department of Mathematics, Kongunadu Arts and Science College (Autonomous), Coimbatore 641029, Tamil Nadu, India
4.
Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulthur 603203, Tamil Nadu, India

Received: 07 May 2023 Revised: 24 July 2023 Accepted: 15 August 2023 Published: 05 September 2023
MSC : 34B10, 35B65, 37L05, 45K05, 47H10, 47N20

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.
- integro-differential equations,
- integrated resolvent operator,
- Lipschitz condition,
- strict solution,
- fixed point theorem
Citation: Kottakkaran Sooppy Nisar, Kasilingam Munusamy, Chokkalingam Ravichandran, Sriramulu Sabarinathan. Interpretation on nonlocal neutral functional differential equations with delay[J]. AIMS Mathematics, 2023, 8(11): 25611-25632. doi: 10.3934/math.20231307

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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.

References

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