Explanipedia

Criteria for Finite-Time Convergence in Discrete Variable-Order Fractional FitzHugh–Nagumo Reaction–Diffusion Systems Open

Nidal Anakira, Iqbal H. Jebri, Iqbal M. Batiha, Mohammad S. Hijazi, Tala Sasa · 2025

This study addresses the problem of finite-time stability (FTS) for a discrete-time FitzHugh–Nagumo reaction–diffusion system (FHN–RDs) governed by a variable-order (VO) Caputo fractional difference operator. The discrete fractional formul…

\(\alpha_\sigma\)-Sets: A Novel Framework for Generalized Topological Structures with Applications in Digital Topology Open

Jamal Oudetallah, Rehab Alharbi, Ala Amourah, Iqbal M. Batiha, Tala Sasa · 2025

This paper introduces ασ-sets as a new class of generalized topological structures that extend α-open sets to countable unions with controlled boundary behavior. We prove these structures form a σ-algebra under union operations and exhibit…

An Analytical and Numerical Approach to Vegetation–Nutrient Dynamics Involving Symbiotic Nitrogen Fixation and the Allee Effect Open

Shaher Momani, Iqbal M. Batiha, Ahmed Bouchenak, Koichi Unami · 2025

This study develops a nonlinear dynamical system with three variables representing the standardized abundances of a leguminous plant, a non-leguminous plant, and a nutrient resource. The system is governed by a set of nonlinear conformable…

Numerical Analysis of a SEIHRD Model for a Hypothetical Ebola Outbreak During the 2025 Hajj Season in Saudi Arabia Open

Abeer A. Al-Nana, Iqbal M. Batiha, Ahmed Bouchenak, Shaimaa Ahmed · 2025

Saudi Arabia, one of the world’s most frequented destinations for foreign visitors and pilgrims—particularly during the Hajj season—faces an elevated risk of infectious disease outbreaks due to the high influx of international travelers. O…

Control Strategies for Mittag-Leffler Synchronization in Variable-Order Fractional FitzHugh-Nagumo Reaction-Diffusion Networks Open

Iqbal H. Jebril, Iqbal M. Batiha, Shaher Momani, Anjan Biswas · 2025

This work presents a synchronization control methodology for Variable Fractional-Order Reaction-Diffusion systems (VFO-RDs), focusing on the FitzHugh-Nagumo model. Using Caputo fractional difference operators with time-dependent orders, we…

Application of Ujlayan-Dixit (UD) Fractional Gamma With Two-Parameters Probability Distribution Open

Iqbal H. Jebril, Iqbal M. Batiha, Nadia Allouch · 2025

The main goal in this research is to use the Ujlayan-Dixit (UD) fractional derivative to generate a new fractional probability density function for the two-parameters gammadistribution, and develop some applications of this new distributio…

Short Note of Linguistic SuperHypersoft Set Open

Takaaki Fujita, Ayman A. Hazaymeh, Iqbal M. Batiha, Anwar Bataihah, Jamal Oudetallah · 2025

Soft sets provide a mathematical framework for decision-making by associating parameters with subsets of a universal set, effectively managing uncertainty and imprecision [6, 7]. Over time, various extensions of soft sets, including Hypers…

Results on the existence of solutions for conformable evolution differential equations with non-local conditions Open

Mazin Aljazzazi, Fakhreddine Seddiki, Iqbal M. Batiha, Ahmed Bouchenak, Rasha Ibrahim Hajaj · 2025

This paper investigates the existence of solutions for conformable evolution differential equations under non-local conditions. Using fixed-point theory and analytical methods, we establish solution existence for equations involving confor…

Refined normality criteria in regionally compact topological domains Open

Iqbal M. Batiha, Praveen Agarwal, Ala Amourah, Hassan S. Al-Zou’bi · 2025

This manuscript presents enhanced formulations of normality in topological domains, extending the groundwork laid by Williams, Harrington, and others. We propose a novel conceptualization of σ-constrained normality and provide refined cond…

Separation Axioms Beyond T2: Novel Properties and Interactions in Non-Regular Spaces Open

Jamal Oudetallah, Wasim Audeh, Manal Al-Labadi, Raja’a Al-Naimi, Iqbal M. Batiha , et al. · 2025

This paper investigates separation axioms that are weaker than the classical Hausdorff condition, examining their relationships in non-regular topological spaces. We focus on spaces that exhibit structural properties characteristic of high…

Analytical Investigation of the Existence and Ulam Stability of Integro-Differential Equations with Conformable Derivatives Under Non-Local Conditions Open

Seddiki Fakhreddine, Ayman A. Hazaymeh, Mazin Aljazzazi, Reham Qaralleh, Anwar Bataihah , et al. · 2025

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, i…

Recurrence Relations for Jacobi Orthogonal Polynomials on the Triangular Domain Open

Iqbal M. Batiha, Wala’a Ahmad Alkasasbeh, Abedallah Rababah, Hamzah O. Al-Khawaldeh, Iqbal H. Jebril · 2025

In this paper, we present recurrence relations for the Jacobi weighted orthogonal polynomials Pn,r(α,β,γ) (u, v, w) with r = 0, 1, . . . , n, where n ≥ 0, defined on the triangular domain T = {(u, v, w) : u, v, w ≥ 0, u + v + w = 1} for va…

REGULARIZED ITERATIVE FDEM: A NUMERICAL APPROACH FOR NONLINEAR CAPUTOFRACTIONAL DIFFERENTIAL EQUATIONS Open

Ramzi B. Albadarneh, Iqbal M. Batiha, Radwan M. Batyha, Shaher Momani · 2025

Stability Analysis of a Fractional-Order Lengyel–Epstein Chemical Reaction Model Open

Khelifa Bouaziz, N. Djeddi, Osama Ogilat, Iqbal M. Batiha, Nidal Anakira , et al. · 2025

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 o…

Nearly Lindelöfness in \(N^{th}\)-Topological Spaces Open

Jamal Oudetallah, Rehab Alharbi, Salsabiela Rawashdeh, Iqbal M. Batiha, Ala Amourah , et al. · 2025

The concepts of approximately Nth-Lindelöf spaces, introduced in [15] and [16], represent weaker forms of single Lindelöf spaces and have since attracted significant attention. In this paper, we revisit these spaces through the lens of a p…

Application of Ujlayan-Dixit Fractional Chi-Square Probability Distribution Open

Iqbal H. Jebril, Raed Hatamleh, Iqbal M. Batiha, Nadia Allouch · 2025

In this study, we take into account the Ujlayan-Dixit (UD) fractional derivative in order to introduce the fractional probability density function for the Chi-Square distribution (CSD), and to establish certain new applications for this di…

Application of Ujlayan-Dixit Fractional Exponential Probability Distribution Open

Iqbal H. Jebril, Raed Hatamleh, Iqbal M. Batiha, Nadia Allouch · 2025

This research aims to present the probability density functions of random variables for exponential distribution by applying a new technique of the Ujlayan-Dixit (UD) fractionalde rivative and to find some basic concepts related to probabi…

Finite-time analysis of epidemic reaction-diffusion models: Stability, synchronization, and numerical insights Open

Iqbal M. Batiha, Nidal Anakira, Issam Bendib, Adel Ouannas, Amel Hioual , et al. · 2025

This study presents an innovative approach to analyzing finite-time stability (FTS) and synchronization (FTSYN) in integer-order reaction-diffusion systems (RDs), particularly in the context of epidemiological modeling. By integrating Gron…

SECURE METRIC DIMENSION OF ALTERNATE SNAKE GRAPHS Open

Basma Mohamed, Iqbal M. Batiha, Nidal Anakira, Mohammad Odeh, Mohammad Shehab , et al. · 2025

We study the NP-hard problem of determining the secure metric dimension of graphs. A resolving set uniquely identifies each vertex by its distance vector to the set; the smallest is the metric basis, and its size is the metric dimension. A…

Trapezoidal Scheme for the Numerical Solution of Fractional Initial Value Problems Open

Iqbal M. Batiha, Hebah F. Alsamad, Iqbal H. Jebril, Hamzah O. Al-Khawaldeh, Wala’a A. Al Kasasbeh , et al. · 2025

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 fractiona…

Some Types of Tri-Lindelöfness Spaces Open

Jamal Oudetallah, Rehab Alharbi, Iqbal M. Batiha, Salsabiela Rawashdeh, Ala Amourah · 2025

In this study, the Lindelöf property of spaces will be examined across three topologies, referred to as tri-Lindelöf spaces. Furthermore, the characteristics of these spaces will be analyzed in relation to Lindelöf spaces. Several theoreti…

Surpassing Taylor method: the generalized Taylor method for solving initial value problems Open

Mohammad W. Alomari, Iqbal M. Batiha, Shaher Momani, Praveen Agarwal, Moahammad Odeh · 2025

This study presents an advancement in the Taylor method through the development of an enhanced, higher-order variant that accelerates series expansion, yielding a refined, implicit formulation with improved accuracy. Both stability and con…

A Comparative Analysis of Numerical Techniques: Euler-Maclaurin vs. Runge-Kutta Methods Open

Mohammad W. Alomari, Iqbal M. Batiha, Abeer A. Al-Nana, Mohammad Odeh, Nidal Anakira , et al. · 2025

This study introduces a novel higher-order implicit correction method derived from the Euler-Maclaurin formula to enhance the approximation of initial value problems. The proposed method surpasses the Runge-Kutta approach in accuracy, stab…

Generalization of the Nonlinear Bernoulli Conformable Fractional Differential Equations with Applications Open

Ahmed Bouchenak, Iqbal M. Batiha, Iqbal H. Jebril, Mazin Aljazzazi, Hamzeh Taha Alkasasbeh , et al. · 2025

In this work, we study a well-known nonlinear fractional differential equation—the nonlinear Bernoulli conformable fractional differential equation. We classify this equation into different categories and establish a fundamental lemma esse…

Advanced solutions for nonlinear fractional equations: a Laplace-Caputo-RKDM approach Open

Nadir Djeddi, Iqbal M. Batiha, Nesrine Harrouche, Mohammed Al‐Smadi, Shaher Momani · 2025

This study proposes a novel framework that combines the Laplace Transform with the reproducing kernel discretization method (RKDM) under the principles of Caputo derivatives to address the challenges of fractional differential equations. B…

Revolutionizing Numerical Approximations: A Novel Higher-Order Implicit Method vs. Runge-Kutta for Initial Value Problems Open

Mohammad W. Alomari, Iqbal M. Batiha, Nidal Anakira, Ala Amourah, Iqbal H. Jebril , et al. · 2025

This work is dedicated to advancing the approximation of initial value problems through the introduction of an innovative and superior method inspired by Taylor’s approach. Specifically, we present an enhanced variant achieved by accelerat…

Global Existence for Heat Equation with Nonlinear and Damping Piecewise Neumann Boundary Condition Open

Iqbal M. Batiha, Zainouba Chebana, Taki-Eddine Oussaeif, Sana Abu-Ghurra, Abeer A. Al-Nana , et al. · 2025

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 p…

Study and Analysis of the Second Order Constant Coefficients and Cauchy-Euler Equations via Modified Conformable Operator Open

Ahmad Bouchenak, Iqbal M. Batiha, Raed Hatamleh, Mazin Aljazzazi, Iqbal H. Jebril , et al. · 2025

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. Further…

Examining finite-time behaviors in the fractional Gray–Scott model: Stability, synchronization, and simulation analysis Open

Shaher Momani, Iqbal M. Batiha, Issam Bendib, Adel Ouannas, Amel Hioual , et al. · 2025

This paper investigates the behavior and stability of the fractional-order Gray–Scott model, with a specific focus on achieving finite-time stability and synchronization. It introduces essential concepts, including the Gamma function, the …

Stability analysis and numerical simulations of a discrete-time epidemic model Open

Iqbal M. Batiha, Maeshal Hijazi, Amel Hioual, Adel Ouannas, Mohammad Odeh , et al. · 2025

This research investigates a discrete epidemic reaction–diffusion model, focusing on the nuances of both local and global stability. By employing second-order difference schemes alongside L1 approximations, we establish a robust numerical …

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