ORIGINAL RESEARCH article
Front. Phys.
Sec. Interdisciplinary Physics
This article is part of the Research TopicMathematical Physics Methods and Advanced Materials in Frontier Applications for Underground EngineeringView all 4 articles
Solving damped elastic inclusions with history-dependent operators and nonconvex-valued perturbations
Provisionally accepted
Hasanen A. Hammad1*
Doha A. Kattan2- 1Sohag University, Sohag, Egypt
- 2King Abduaziz University, Rabegh, Saudi Arabia
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In this paper, we investigate damped elastic inclusion systems characterized by nonconvex-valued perturbations, the summation of dual multivalued mappings, and history-dependent operators. By extending standard convex frameworks, these perturbations facilitate the modeling of discontinuous and complex dynamics often found in real-world systems. Our primary contribution is the derivation of a novel existence theorem for mild solutions under suitable con-ditions. Lastly, the proposed theoretical results are validated through a detailed examination of elastic feedback control systems as an application.
Keywords: damped elastic inclusion, fixed point, mild solution, Nonlinear equation, Perturbation approach
Received: 19 Dec 2025; Accepted: 04 Feb 2026.
Copyright: © 2026 A. Hammad and Kattan. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Hasanen A. Hammad
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