Emad A. Az-Zo'bi

Mu’tah University · Department of Mathematics and Statistics

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.