Emad A. Az-Zo'bi

Mutah University · Department of Mathematics and Statistics

This study aims to detect the level of challenges facing teachers in applying Internet of Things (IoT) in the educational process. It also investigates the teachers' perceptions regarding the importance of using IoT in the educational process. This study adopts a quantitative approach to analyse the use of IoT amongst Saudi secondary school teacher...

This work focuses on finding closed-form analytic solutions of a higher-dimensional fractional model, in conformable sense, known by the (4+1)-dimensional Fokas equation. Fractional partial differential equations (FPDEs) and systems can describe heritable real-world occurrences. However, solving such models can be difficult, especially for nonlinea...

Performance assessment is a valuable method of evaluating students' understanding and abilities in educational settings. It involves measuring what students know and can do by having them demonstrate their skills, knowledge, and competencies through various tasks, projects, or activities. Performance assessments are designed to assess a student's a...

Under the consideration of computational software Mathematica on the basis of extended simple equation method, constructed the periodic wave soliton solutions for nonlinear Zakharov–Kuznetsov modified equal width equation. In this study, constructed soliton solutions included periodic singular solitons, bright solitons, kink solitons, anti-kink sol...

In this paper, a collocation method based on the Dejdumrong polynomial matrix approach was used to estimate the solution of higher-order pantograph-type linear functional differential equations. The equations are considered with hybrid proportional and variable delays. The proposed method transforms the functional-type differential equations into m...

Nematicons upgrade the recognition of light localization in the reorientation of non-local media. the current research employs a powerful integral scheme using a different procedure, namely, the modified simple equation method (MSEM), to analyze nematicons in liquid crystals from the controlling model. The expanded MSEM is investigated to enlarge t...

The improved F-expansion method is used in this work to investigate the nonlinear Landau–Ginsberg–Higgs (NLLGH) equation. The nonlinear Landau–Ginsberg–Higgs equation mainly depicts nonlinear wave propagation, categorizes wave velocity, and materializes several phenomena via a dispersive system. New solitary wave structures are extracted by combini...

This study aims to explore the precise resolution of the nonlinear Benjamin Bona Mahony Burgers (BBMB) equation, which finds application in a variety of nonlinear scientific disciplines including fluid dynamics, shock generation, wave transmission, and soliton theory. Within this paper, we employ two versatile methodologies, specifically the extend...

One of the most influential physical models for explaining the transmission of an optical soliton in optical fibre theory is the nonlinear Schrödinger equation (NLSE). Due to its many potential uses in communications and ultrafast signal routing systems, chiral soliton propagation in nuclear physics is a subject that holds a great deal of interest....

The current investigation examines the fractional forced Korteweg-de Vries (FF-KdV) equation, a critically significant evolution equation in various nonlinear branches of science. The equation in question and other associated equations are widely acknowledged for their broad applicability and potential for simulating a wide range of nonlinear pheno...

The Sharma–Tasso–Olver–Burgers (STOB) equation is a nonlinear partial differential equation that appears in many branches of science, engineering and describes significant phenomena including wave propagation and fluid dynamics. The STOB equation characteristics and solutions for the nonlinear situation are thoroughly examined in this research work...

This study investigates the exact solutions of the time-fractional (3+1)-dimensional combined Korteweg–de Vries Benjamin–Bona–Mahony (KdV-BBM) equation. The considered model describes the long surface gravity waves of small amplitude, which portrays the two-way propagation of waves. The modified generalized Kudryashov method and the exp(-φ(ξ\docume...

This study aims to examine the nonlinear partial differential equation known as the (1+1)-dimensional generalized Kundu-Eckhaus equation with extra-dispersion, which is used to model the transmission of ultra-short femtosecond pulses in an optical fiber. Two versatile techniques, namely the extended $(\frac{G'}{G^{2}})$-expansion as well as the ext...

The combined Korteweg-de Vries (KdV)-modified KdV (mKdV) equation widely appears as an integrable model in a wide range of interacting physical phenomena to explore their nonlinear dynamical features with geometrical structures. In this work, we present a comprehensive physical analysis of a bunch of solitary waves associated with a combined KdV-mK...

The use of renewable energy sources is leading the charge to solve the world’s energy problems, and non-Newtonian nanofluid dynamics play a significant role in applications such as expanding solar sheets, which are examined in this paper, along with the impacts of activation energy and solar radiation. We solve physical flow issues using partial di...

Nonlinear evolution equations are employed in the representation of diverse intricate physical events, and the identification of precise solutions for these equations holds significance about their practical implementations. One of the significant challenges is the identification of traveling wave solutions inside established nonlinear evolution sy...

In this paper, we define and study the notion of hereditary class on nearly μ-Lindelöf space. Moreover, we study the effects of some types of continuity of hereditary class on nearly μ-Lindelöf space by properties of the function. Also, more variations between these spaces and some known spaces are investigated .

The aim of current investigation is to explore the two-dimensional Darcy flow of second grade fluid with homogenous and heterogeneous reactions toward a porous curved stretching surface. The thermal features the bioconvective flow are observed with the impact of joule heating, nonlinear thermal radiation, and non-uniform heat source/sink. The therm...

This paper conducts an extensive comparative analysis of numerical methods employed in modeling blood flow through arteries with Magnetohydrodynamics (MHD) and hybrid nanofluids. The study investigates the effectiveness and precision of distinct numerical approaches: Akbari Ganji’s Method (AGM), Fourth-Order Runge–Kutta (RK4), Finite Volume Method...

This analysis examines the time-fractional mixed hyperbolic-elliptic p-system of conservation laws by applying the new extended direct algebraic method. The p-system with generalized cubic van der Waals flux, and potential applications in the field of compressible isothermal viscosity-capillarity fluids, is investigated. In particular, this issue d...

In this study, the new complex wave solutions of the perturbed Fokas-Lenells (p-FL) equation, which has applications in nonlinear optical fibers are obtained using a new extended direct algebraic method. This model represents recent electronic communications like Internet blogs, facebook communication and twitter comments. The obtained solutions ar...

The endoscopy of a coronary arterial segment having a symmetric emergence of plaque at its innermost region is numerically modeled via computational fluid dynamics toolbox Open-FOAM. The considered left coronary artery for this model has a radius of 2 mm and span of 10 mm. The formation of plaque inside the artery that is a stenosis has length 2 mm...

Ordinary differential equations (ODEs) are fundamental tools for modeling and understanding a wide range of chemistry, physics, and biological phenomena. However, solving complex ODEs often presents significant challenges, necessitating advanced numerical approaches beyond traditional analytical techniques. Thus, a novel machine learning (ML)-based...

The primary objective of this study aims to carry out a more thorough investigation into a fractional nonlinear double dispersive equation that is used to represent wave propagation in an elastic, inhomogeneous Murnaghan’s rod. By Murnaghan’s rod, we mean the materials, which include the constitutive constant, Poisson ratio, and Lame’́s coefficient...

In this paper, we study linear and nonlinear mixed convection, activation energy, and heat radiation effects caused by nanoparticles. This study aims to improve the understanding of how nanofluids behave in the presence of rotating disks and develop more efficient and effective cooling technologies. The flow problem consisted of partial differentia...

In fluid dynamics, mixed-type systems of conservation laws model a wide range of phase transition problems in compressible media. This analysis studies analytically the time-fractional mixed-type hyperbolic-elliptic van der Waals p-system with generalized cubic flux function for the first time. For this purpose, the expanded ansatz method is introd...

In this study, we investigate the interactions of a hybrid nanofluid on a curved surface that is being stretched. The magnetic field is perpendicular to the flow and interacts with a mixture of molybdenum disulfide and argentum nanoparticles suspended in pure water, forming a hybrid nanomaterial. Our investigation considers heat transport analysis...

The purpose of this manuscript is to investigate the precise soliton solution of the \((1 + 1)\)-dimensional Sharma–Tasso–Olver–Burgers equation. This study thoroughly explores the characteristics and solutions of this nonlinear equation. To pinpoint the exact soliton solution, we employ analytical techniques, specifically the \(\exp (-\phi (\xi ))...

Complex fuzzy sets (CFSs) have recently emerged as a potent tool for expanding the scope of fuzzy sets to encompass wider ranges within the unit disk in the complex plane. This study explores complex fuzzy numbers and introduces their application for the first time in the literature to address a complex fuzzy partial differential equation that invo...

Complex fuzzy sets (CFSs) have recently emerged as a potent tool for expanding the scope of fuzzy sets to encompass wider ranges within the unit disk in the complex plane. This study explores complex fuzzy numbers and introduces their application for the first time in the literature to address a complex fuzzy partial differential equation that invo...

This study aimed to investigate the impact of blended learning on students' achievement and their motivation to learn limits and differentiation. To achieve the research goal, the researchers employed a quasi-experimental methodology. The study's population consisted of (65) male students from one of secondary school at the directorate of education...

This study aimed to investigate the impact of blended learning on students' achievement and their motivation to learn limits and differentiation. To achieve the research goal, the researchers employed a quasi-experimental methodology. The study's population consisted of (65) male students from one of secondary school at the directorate of education...

Citation: Ur Rahman, R.; Faridi, W.A.; El-Rahman, M.A.; Taishiyeva, A.; Myrzakulov, R.; Az-Zo'bi, E.A. The Sensitive Visualization and Generalized Fractional Solitons'Construction for Regularized Long-Wave Governing Model. Fractal Fract. 2023, 7, 136. Abstract: The solution of partial differential equations has generally been one of the most-vital...

We define the notions of weakly μ-countably compactness and nearly μ-countably compactness denoted by Wμ-CC and Nμ-CC as generalizations of μ-compact spaces in the sense of Csaśzaŕ generalized topological spaces. To obtain a more general setting, we define Wμ-CC and Nμ-CC via hereditary classes. Using μθ-open sets, μ-regular open sets, and μ-regula...

The current research aims to implement the numerical results for the Holling third kind of functional response delay differential model utilizing a stochastic framework based on Levenberg-Marquardt backpropagation neural networks (LVMBPNNs). The nonlinear model depends upon three dynamics, prey, predator, and the impact of the recent past. Three di...

In this research, the new auxiliary equation method (NAEM) for higher order nonlinear fractional Huxley equation is being employed to extricate the novel soliton solutions using Beta and M-Truncated fractional derivatives. For waves of finite amplitude, the Huxley equation demonstrates a substantial transfer of spectrum energy. A comparison of the...

This analysis utilizes the generalized Riccati simple equation method to construct nematicons in liquid crystals from its governing system. A new type of nonlinearity is studied for the first time in the context of liquid crystals. It is the nonlinear quadruple power law. The fractional version of the governed model, with conformable sense, is cons...

The current study suggests a new generalisation of highly dispersive nonlinear Schrödinger-type equation (NLSE) with perturbation terms. With polynomial refractive index, known by cubic-quintic-septic (CQS) law and Hamiltonian-type cubic perturbation terms, the new model includes eighth-order dispersion term. The generalised Riccati simplest equati...

The telecommunications revolution finds its foundation thanks to new service offerings including voice, images, security of computer data and much more. Thereby, telecommunications can be defined as the transmission of information at a distance using electronic, computer, wired, optical or electromagnetic technologies. At an expense of these charac...

The current analysis employs the Riccati and modified simple equation methods to retrieve new optical solitons for highly dispersive nonlinear Schr"{o}dinger-type equation (NLSE). With cubic-quinticseptic law (also known as a polynomial) of refractive index and perturbation terms having cubic nonlinearity, 1-optical solitons in the form of hyperbol...

In this paper, we examined four different forms of generalized (2+1)-dimensional Boussinesq–Kadomtsev–Petviashvili (B-KP)-like equations. In this connection, an accurate computational method based on the Riccati equation called sub-equation method and its Bäcklund transformation is employed. Using this method, numerous exact solutions that do not e...

In this article, (2+1)-dimensional Ito equation that models waves motion on shallow water surfaces is analyzed for exact analytic solutions. Two reliable techniques involving the simplest equation and modified simplest equation algorithms are utilized to find exact solutions of the considered equation involving bright solitons, singular periodic so...

This work provides a technical applied description of the residual power series method (RPSM) to develop a fast and accurate algorithm for mixed hyperbolic–elliptic systems of conservation laws with Riemann initial datum. The RPSM does not require discretization, reduces the system to an explicit system of algebraic equations and consequently of ma...

This paper studies the propagation of the short pulse optics model governed by the higher-order nonlinear Schrödinger equation (NLSE) with non-Kerr nonlinearity. Exact one-soliton solutions are derived for a generalized case of the NLSE with the aid of software symbolic computations. The modified Kudryashov simple equation method (MSEM) is employed...

his paper studies the propagation of the short pulse optics model governed by the higher order nonlinear Schrödinger equation (NLSE) with non-Kerr nonlinearity. Exact one-soliton solutions are derived for a generalized case of the NLSE with the aid of software symbolic computations. The modified Kudryashov simple equation method (MSEM) is employed...

In the current analysis, the conformable generalized Kudryashov equation of pulses propagation with power non-linearity is processed. The considered higher order equation represents a generalized mathematical model of many well-known ones in nonlinear media. A variety of multiple kinks, bi-symmetry, periodic, singular, bright and dark optical solit...

The conformable derivative and adequate fractional complex transform are implemented to discuss the fractional higher-dimensional Ito equation analytically. The Jacobi elliptic function method and Riccati equation mapping method are successfully used for this purpose. New exact solutions in terms of linear, rational, periodic and hyperbolic functio...

In this paper, with the aid of the Mathematica package, several classes of exact analytical solutions for the time-fractional (2+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{...

The main objective of our analysis is to modify the reduced differential transform method (RDTM) to be applicable for a wide range of nonlinear partial differential equations. The Adomian polynomials are employed to overcome the huge size and complexity of computing reduced differential transforms, and new generalizations of transformed formulas ar...

This work deals with a new modified version of the Adomian-Rach decomposition method (MDM). The MDM is based on combining a series solution and decomposition method for solving nonlinear differential equations with Adomian polynomials for nonlinearities. With application to a class of nonlinear oscillators known as the Lienard-type equations, conve...

The simple equation method and modified simple equation method are employed to seek exact traveling wave solutions to the (1 + 1)‐dimensional van der Waals gas system in the viscosity‐capillarity regularization form. Under the help of Mathematica, new classes of kink solutions are derived. Numerical simulations with special choices of the free para...

In this study, we propose a developed semi-analytic technique, so called the generalized residual power series method, to process higher-dimensional linear and nonlinear partial differential equations. The obtained solution is expressed in a form of rapidly convergent power series with easily computable coefficients. Solution can, in turn, be terme...

A residual power series scheme is developed for mixed-type p-system of conservation laws. The residual power series method (RPSM) does not require discretization, reduces the system to an explicit system of algebraic equations and consequently of massive computations. Convergence hypotheses are discussed and error bounds of exponential rates are de...

The aim of the present analysis is to apply two relatively recent methods, reduced differential transform method (RDTM) and differential transform method (DTM), for the solution of balance law systems. New generalized transformed formulas are derived. The new approaches provided the solution in the form of a rapidly convergent series with easily co...

The aim of the present analysis is to apply the modified decomposition method (MDM) for the solution of isentropic flow of an inviscid gas model (IFIG). The modification form based on a new formula of Adomian polynomials (AP’s). The new approach provides the solution in the form of a rapidly convergent series with easily computable components and n...

The aim of the present analysis is to apply the modified decomposition method (MDM) for the solution of isentropic flow of an inviscid gas model (IFIG). The modification form based on a new formula of Adomian’s polynomials (APs). The new approach provides the solution in the form of a rapidly convergent series with easily computable components and...

Our interest in this paper is to define and study the concept of the fundamental group of intuitionistic fuzzy topological spaces, which depends on the concepts of intuitionistic fuzzy sets and intuitionistic fuzzy topology. Indeed, the paper is a generalization of the fundamental group of fuzzy topological spaces. © 2014 Emad A. Az-Zo'bi, Mohammad...

In this paper, We apply a relatively new semi-analytic technique called the reduced differential transform method (RDTM) to solve the generalized Burger's-Huxley equation and some special cases. The definition and basic theorems in additive to new generalized transforms of RDTM are investigated. The RDTM produces an approximate solution without any...

In this paper, we apply Adomian decomposition method (ADM) to develop a fast and accurate algorithm for systems of conservation laws of mixed hyperbolic elliptic type. The solutions of our model equations are calculated in the form of convergent power series with easily computable components. The results obtained are compared with our Modification...

In this paper, the Laplace Decomposition Method (LDM) is improved to obtain approximate analytical solutions of linear and nonlinear differential equations and systems. Based on a new Algorithm of calculating Adomian polynomial's (AP's), the proposed algorithm is efficient and simple to apply. Some illustrative examples are presented and the result...

In this paper, we propose a new convergence proof of the Adomian’s decomposition method (ADM), applied to the generalized nonlinear system of partial differential equations (PDE’s) based on new formula for Adomian polynomials. The decomposition scheme obtained from the ADM yields an analytical solution in the form of a rapidly convergent series for...

We prove an inequality of the form ∥x (k) ∥ 2 ≤A∥x (r) ∥ 2 +B∥x∥ 2 , for k,r∈ℕ∪{0}, 0≤k<r. For a given A≥0 we find the infimum B≥0 such that the inequality holds for all sufficiently smooth functions.

We prove an inequality of the form for k, r ∈ N ∪{0}, 0 ≤ k<r.For a given A ≥ 0 we find the infimum B ≥ 0 such that (0.1) holds for all sufficiently smooth functions.