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Research Article | Open Access

Solving delay integro-differential inclusions with applications

Maryam G. Alshehri1, Hassen Aydi2,3( ), Hasanen A. Hammad4,5,6( )
Department of Mathematics, Faculty of Science, University of Tabuk, P. O. Box741, Tabuk 71491, Saudi Arabia
Institut Supérieur d'Informatique et des Techniques de Communication, Université de Sousse, H. Sousse 4000, Tunisia
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa
Department of Mathematics, College of Science, Qassim University, Buraydah 52571, Saudi Arabia
Department of Mathematics, Saveetha School of Engineering, SIMATS, Saveetha University, Chennai 602105, India
Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt
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Abstract

This work primarily delves into three key areas: the presence of mild solutions, exploration of the topological and geometrical makeup of solution sets, and the continuous dependency of solutions on a second-order semilinear integro-differential inclusion. The Bohnenblust-Karlin fixed-point method has been integrated with Grimmer's theory of resolvent operators. Ultimately, the study delves into a mild solution for a partial integro-differential inclusion to showcase the achieved outcomes.

Keywords

fixed point techniquesemilinear integro-differential inclusionmild solutionpartial integro-differential inclusion
CLC number: 26A33, 26D15, 47H08, 47H10

References

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AIMS Mathematics
Volume 9 Issue 6,
May 2024
Pages 16313-16334
DOI: 10.3934/math.2024790

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Cite this article:
Alshehri MG, Aydi H, Hammad HA. Solving delay integro-differential inclusions with applications. AIMS Mathematics, 2024, 9(6): 16313-16334. https://doi.org/10.3934/math.2024790

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Received: 15 February 2024
Revised: 12 April 2024
Accepted: 16 April 2024
Published: 09 May 2024
©2024 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)