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All Journal International Journal of Robotics and Control Systems
Bataihah, Anwar
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Control & Systems Engineering Electrical & Electronics Engineering

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Global Existence for Heat Equation with Nonlinear and Damping Piecewise Neumann Boundary Condition Batiha, Iqbal M.; Chebana, Zainouba; Oussaeif, Taki-Eddine; Abu-Ghurra, Sana; Al-Nana, Abeer; Bataihah, Anwar; Jebril, Iqbal H.
International Journal of Robotics and Control Systems Vol 5, No 2 (2025)
Publisher : Association for Scientific Computing Electronics and Engineering (ASCEE)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31763/ijrcs.v5i2.1653

Abstract

The Columbia space shuttle catastrophe in 2003 served as the inspiration for this paper’s improved mathematical model, which includes a nonlinear damping Neumann boundary condition. By creating and examining a modified heat equation with piecewise nonlinear source terms and damping Neumann boundary conditions, the study seeks to investigate the incident’s heat transport dynamics. To ensure that the problem is well-posed, we provide strong mathematical arguments for the existence of solutions both locally and globally. In addition, we use numerical simulations to show how the nonlinear boundary conditions affect heat dissipation and to confirm the theoretical results. The findings advance our knowledge of thermal modeling in aircraft applications and offer greater insights into heat propagation under such conditions.
Analytical Investigation of the Existence and Ulam Stability of Integro-Differential Equations with Conformable Derivatives Under Non-Local Conditions Fakhreddine, Seddiki; Hazaymeh, Ayman A; Aljazzazi, Mazin; Qaralleh, Reham; Bataihah, Anwar; Batiha, Iqbal M.; Hajaj, Rasha Ibrahim
International Journal of Robotics and Control Systems Vol 5, No 2 (2025)
Publisher : Association for Scientific Computing Electronics and Engineering (ASCEE)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31763/ijrcs.v5i2.1828

Abstract

This study examines an integro-differential equation involving fractional conformable derivatives and non-local conditions. It proves the existence and uniqueness of mild solutions by applying the Banach fixed-point theorem. Furthermore, it demonstrates a notable result about the existence of at least one solution, backed by conditions based on the Krasnoselskii fixed-point theorem. The investigation also explores the Ulam stability of integro-differential equations. To highlight the practical relevance and robustness of the findings, an illustrative example is provided.
Co-Authors Abu-Ghurra, Sana Al-Nana, Abeer Aljazzazi, Mazin Batiha, Iqbal M. Chebana, Zainouba Fakhreddine, Seddiki Hajaj, Rasha Ibrahim Hazaymeh, Ayman A Jebril, Iqbal H. Oussaeif, Taki-Eddine Qaralleh, Reham