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All Journal Journal of Robotics and Control (JRC) International Journal of Robotics and Control Systems
Jebril, Iqbal H.
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Aerospace Engineering Computer Science & IT Control & Systems Engineering Electrical & Electronics Engineering Mechanical Engineering

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Euler-Maclaurin Method for Approximating Solutions of Initial Value Problems Alomari, Mohammad W.; Batiha, Iqbal M.; Alkasasbeh, Wala’a Ahmad; Anakira, Nidal; Jebril, Iqbal H.; 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.v5i1.1560

Abstract

This work is dedicated to advancing the approximation of initial value problems through the introduction of an innovative and superior method inspired by the Euler-Maclaurin formula. This results in a higher-order implicit corrected method that outperforms Taylor’s and Runge–Katta’s methods in terms of accuracy. We derive an error bound for the Euler-Maclaurin higher-order method, showcasing its stability, convergence, and greater efficiency compared to the conventional Taylor and Runge-Katta methods. To substantiate our claims, numerical experiments are provided, highlighting the exceptional efficiency of our proposed method over the traditional well-known methods.
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.
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.
Study and Analysis of the Second Order Constant Coefficients and Cauchy-Euler Equations via Modified Conformable Operator Bouchenak, Ahmad; Batiha, Iqbal M.; Hatamleh, Raed; Aljazzazi, Mazin; Jebril, Iqbal H.; Al-Horani, Mohammed
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.v5i2.1577

Abstract

In this paper, we are concerned with a new modified conformable operator. Such an operator makes the study very easy in fractional calculus because it satisfies the most properties as the usual derivative and gives exact solutions. Furthermore, we will analyze and study the second-order fractional linear homogeneous differential equation with constant coefficients, which has two reasons for the importance of these types of differential equations. First of all, they often arise in applications. Second, it is relatively easy to find fundamental sets of solutions to these equations. In addition, we will also analyze the related fractional Cauchy–Euler type equation, which is used in various fields, physics, engineering, etc. Finally, as an application, we will illustrate the method on some numerical examples of the mentioned type of fractional differential equations.
Fractional-Order Discrete Predator–Prey System of Leslie Type: Existence, Stability, and Numerical Simulation Jebril, Iqbal H.; Lakehal, Aymen; Benyoussef, Soufiane
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.v5i2.1864

Abstract

This study explores a fractional-order (FO) discrete predator prey (PP) system of Leslie type (LT) by incorporating fractional differences in the Caputo-Fabrizio-Riemann (CFR) sense. We rigorously establish the existence and uniqueness of solutions and provide a comprehensive stability analysis. A novel numerical scheme is developed to approximate the system’s dynamics, yielding deeper insights into PP interactions under FO effects. Furthermore, we validate our theoretical findings using numerical simulations, which confirm the robustness and accuracy of the proposed model. The results underline the significance of fractional calculus (FC) in ecological modeling and pave the way for future investigations in population dynamics.
Trapezoidal Scheme for the Numerical Solution of Fractional Initial Value Problems Batiha, Iqbal M.; Alsamad, Hebah F.; Jebril, Iqbal H.; Al-Khawaldeh, Hamzah O.; Kasasbeh, Wala’a A. Al; Momani, Shaher
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.v5i2.1795

Abstract

The purpose of this study is to recall the main concepts and definitions in relation to the fractional calculus. In light of this overview, we will propose a novel fractional version of the so-called Trapezoid method named by the fractional Trapezoid method. Such a method will then be used to numerically solve the analog version of the initial value problems called fractional initial value problem FIVPs. As consequences of the proposed numerical approach, several numerical examples will be illustrated to verify the efficiency of the proposed numerical approach.
Co-Authors Abdelnebi, Amira Abu-Ghurra, Sana Al-Horani, Mohammed Al-Khawaldeh, Hamzah O. Al-Nana, Abeer Aljazzazi, Mazin Alkasasbeh, Wala’a Ahmad Alkhazaleh, Shawkat Allouch, Nadia Alomari, Mohammad W. Alsamad, Hebah F. Anakira, Nidal Bataihah, Anwar Batiha, Iqbal Batiha, Iqbal M. Bendib, Issam Benyoussef, Soufiane Bouchenak, Ahmad Chebana, Zainouba Hatamleh, Raed Kasasbeh, Wala’a A. Al Lakehal, Aymen Momani, Shaher Ouannas, Adel Oussaeif, Taki-Eddine Shqair, Mohammed