Solving delay integro-differential inclusions with applications

Maryam G. Alshehri; Hassen Aydi; Hasanen A. Hammad; Maryam G. Alshehri; Hassen Aydi; Hasanen A. Hammad

doi:10.3934/math.2024790

AIMS Mathematics

2024, Volume 9, Issue 6: 16313-16334. doi: 10.3934/math.2024790

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Research article

Solving delay integro-differential inclusions with applications

1.
Department of Mathematics, Faculty of Science, University of Tabuk, P. O. Box741, Tabuk 71491, Saudi Arabia
2.
Institut Supérieur d'Informatique et des Techniques de Communication, Université de Sousse, H. Sousse 4000, Tunisia
3.
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa
4.
Department of Mathematics, College of Science, Qassim University, Buraydah 52571, Saudi Arabia
5.
Department of Mathematics, Saveetha School of Engineering, SIMATS, Saveetha University, Chennai 602105, India
6.
Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt

Received: 15 February 2024 Revised: 12 April 2024 Accepted: 16 April 2024 Published: 09 May 2024
MSC : 26A33, 26D15, 47H08, 47H10

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.
- fixed point technique,
- semilinear integro-differential inclusion,
- mild solution,
- partial integro-differential inclusion
Citation: Maryam G. Alshehri, Hassen Aydi, Hasanen A. Hammad. Solving delay integro-differential inclusions with applications[J]. AIMS Mathematics, 2024, 9(6): 16313-16334. doi: 10.3934/math.2024790

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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.

References

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