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All Journal Journal of Robotics and Control (JRC) International Journal of Robotics and Control Systems
Alkhazaleh, Shawkat
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Aerospace Engineering Computer Science & IT Control & Systems Engineering Electrical & Electronics Engineering Mechanical Engineering

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On New Results of Stability and Synchronization in Finite-Time for Fitiz-Nagamo Model Using Grownal Inequality and Lyapunov Function Batiha, Iqbal M.; Bendib, Issam; Ouannas, Adel; Jebril, Iqbal H.; Alkhazaleh, Shawkat; Momani, Shaher
Journal of Robotics and Control (JRC) Vol. 5 No. 6 (2024)
Publisher : Universitas Muhammadiyah Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18196/jrc.v5i6.23211

Abstract

Ionic diffusion across cytomembranes plays a critical role in both biological and chemical systems. This paper reexamines the FitzHugh-Nagumo reaction-diffusion system, specifically incorporating the influence of diffusion on the system’s dynamics. We focus on the system’s finite-time stability, demonstrating that it achieves and maintains equilibrium within a specified time interval. Unlike asymptotic stability, which ensures long-term convergence, finite-time stability guarantees rapid convergence to equilibrium, a crucial feature for real-time control applications. We prove that the equilibrium point of the FitzHugh-Nagumo system exhibits finite-time stability under certain conditions. In particular, we provide a criterion for finite-time stability and derive results using new lemmas and a theorem to guide the system’s design for reliable performance. Additionally, the paper discusses finite-time synchronization in reaction-diffusion systems, emphasizing its importance for achieving coherent dynamics across distributed components within a finite time. This approach has significant implications for fields requiring precise control and synchronization, such as sensor networks and autonomous systems. Practical simulations are presented to elucidate the theoretical principles discussed earlier, using the finite difference method (FDM) implemented in MATLAB.
Computational Approaches to Two-Energy Group Neutron Diffusion in Cylindrical Reactors Batiha, Iqbal; Abdelnebi, Amira; Shqair, Mohammed; Jebril, Iqbal H.; Alkhazaleh, Shawkat; Momani, Shaher
Journal of Robotics and Control (JRC) Vol. 5 No. 6 (2024)
Publisher : Universitas Muhammadiyah Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18196/jrc.v5i6.23392

Abstract

This study addresses the critical need for accurate neutron diffusion modeling in cylindrical reactors, focusing on the two-energy groups neutron diffusion system. Such modeling is essential for optimizing reactor design and safety in nuclear engineering. The research primarily aims to enhance computational methods by transitioning from a traditional integer-order model to a more sophisticated fractional-order model, which can capture complex physical phenomena with greater precision. The study employs the Laplace Transform Method (LTM) to first solve the integer-order system and then extends this approach to a fractional-order system using the Caputo derivative, a method well-suited for systems with memory effects. To efficiently solve the resulting fractional-order model, we introduce the Modified Fractional Euler Method (MFEM), designed to improve numerical accuracy and stability. The effectiveness of this approach is demonstrated through specific numerical applications, such as simulating neutron flux distributions, which validate the model’s accuracy and its potential impact on advancing reactor physics. These applications showcase the practical relevance of the proposed methods and their contribution to improving nuclear reactor simulations.
Fractional Approach to Two-Group Neutron Diffusion in Slab Reactors Batiha, Iqbal M.; Allouch, Nadia; Shqair, Mohammed; Jebril, Iqbal H.; Alkhazaleh, Shawkat; Momani, Shaher
International Journal of Robotics and Control Systems Vol 5, No 1 (2025)
Publisher : Association for Scientific Computing Electronics and Engineering (ASCEE)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31763/ijrcs.v5i1.1524

Abstract

The two-energy neutron diffusion model in slab reactors characterizes neutron behavior across two energy groups: fast and thermal. Fast neutrons, generated by fission, decelerate through collisions, transitioning into thermal neutrons. This model employs diffusion equations to compute neutron flux distributions and reactor parameters, thereby optimizing reactor design and safety to ensure efficient neutron utilization and stable, sustained nuclear reactions. The primary objective of this research is to explore both analytical and numerical solutions to the two-energy neutron diffusion model in slab reactors. Specifically, we will utilize the Laplace transform method for an analytical solution of the two-energy neutron diffusion model. Subsequently, employing the Caputo differentiator, we transform the original neutron diffusion model into its fractional-order equivalents, yielding the fractional-order two-energy group neutron diffusion model in slab reactors. To address the resulting fractional-order system, we develop a novel approach aimed at reducing the 2β-order system to a β-order system, where β ∈ (0, 1]. This transformed system is then solved using the Modified Fractional Euler Method (MFEM), an advanced variation of the fractional Euler method. Finally, we present numerical simulations that validate our results and demonstrate their applicability.
Co-Authors Abdelnebi, Amira Allouch, Nadia Batiha, Iqbal Batiha, Iqbal M. Bendib, Issam Jebril, Iqbal H. Momani, Shaher Ouannas, Adel Shqair, Mohammed