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Research Article | Open Access

New interpretation of topological degree method of Hilfer fractional neutral functional integro-differential equation with nonlocal condition

Kanagaraj Muthuselvan1Baskar Sundaravadivoo1Suliman Alsaeed2,3Kottakkaran Sooppy Nisar3,4( )
Department of Mathematics, Alagappa University, Karaikudi 630004, Tamil Nadu, India
Applied Sciences Collage, Department of Mathematical Sciences, Umm Al-Qura University, P.O. Box 715, Makkah 21955, Saudi Arabia
Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia
School of Technology, Woxsen University- Hyderabad-502345, Telangana State, India
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Abstract

This manuscript deals with the concept of Hilfer fractional neutral functional integro-differential equation with a nonlocal condition. The solution representation of a given system is obtained from the strongly continuous operator, linear operator and bounded operator, as well as the Wright type of function. The sufficient and necessary conditions for the existence of a solution are attained using the topological degree method. The uniqueness of the solution is attained by Gronwall's inequality. Finally, we employed some specific numerical computations to examine the effectiveness of the results.

CLC number: 34A08, 34A12, 46B80

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AIMS Mathematics
Pages 17154-17170

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Cite this article:
Muthuselvan K, Sundaravadivoo B, Alsaeed S, et al. New interpretation of topological degree method of Hilfer fractional neutral functional integro-differential equation with nonlocal condition. AIMS Mathematics, 2023, 8(7): 17154-17170. https://doi.org/10.3934/math.2023876

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Received: 17 January 2023
Revised: 11 March 2023
Accepted: 27 March 2023
Published: 15 July 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)