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All Journal Journal of Robotics and Control (JRC) International Journal of Robotics and Control Systems
Batiha, Iqbal M.
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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.
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.
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.
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.
Stability Analysis of a Fractional-Order Lengyel–Epstein Chemical Reaction Model Bouaziz, Khelifa; Djeddi, Nadhir; Ogilat, Osama; Batiha, Iqbal M.; Anakira, Nidal; Sasa, Tala
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.v5i2.1848

Abstract

In this paper, we stady a mathematical model based on a system of fractional-order differential equations to describe the dynamics of the Lengyel–Epstein chemical reaction, which is well known for exhibiting oscillatory behavior. The use of fractional derivatives allows in chemical processes compared to classical integer-order models. We specifically focus on analyzing the stability of the system’s positive equilibrium point by applying fractional calculus techniques. The stability conditions are derived and discussed in the context of the fractional-order parameters. To validate the theoretical findings, we perform numerical simulations using the Forward Euler method adapted for fractional-order systems. These simulations illustrate the impact of the fractional order on the system’s dynamic behavior and confirm the analytical results regarding equilibrium stability.
Co-Authors 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 Bendib, Issam Bouaziz, Khelifa Bouchenak, Ahmad Chebana, Zainouba Djeddi, Nadhir Fakhreddine, Seddiki Hajaj, Rasha Ibrahim Hatamleh, Raed Hazaymeh, Ayman A Jebril, Iqbal H. Kasasbeh, Wala’a A. Al Momani, Shaher Ogilat, Osama Ouannas, Adel Oussaeif, Taki-Eddine Qaralleh, Reham Sasa, Tala Shqair, Mohammed