Azza Alshehry

• Doctor of Education
• Riyadh at Princess Nourah bint Abdulrahman University

This investigation focuses on the study of the fractional damped Burgers’ equation by using the natural residual power series method coupled with the new iteration transform method in the context of the Caputo operator. The equation of Burgers under the damped context is useful when studying one-dimensional nonlinear waves involving damping effect,...

This study presented a comprehensive analysis of nonlinear fractional systems governed by the advection-dispersion equations (ADE), utilizing the Mohand transform iterative method (MTIM) and the Mohand residual power series method (MRPSM). By incorporating the Caputo fractional derivative, we enhanced the modeling capability for fractional-order di...

Consider a commutative Z2-graded ring (R=R0⨁R1). Consequently, each element (x∈R) can be uniquely expressed as x=x0+x1, where x0∈R0 and x1∈R1. For any x∈R, we consider the function N(x)=x02−x12. In this work, we examine the properties of N and utilize them to derive new results. Moreover, we apply this function to establish concepts such as N-prime...

In this research study, we focus on the generalized regularized long wave equation and the modified regularized long wave equation, which play pivotal roles in characterizing plasma waves in oceans and ion acoustic waves in shallow water, a domain deeply rooted in physical phenomena. Employing two computational techniques, namely, the optimal auxil...

Purpose The purpose of this study is to solve two unique but difficult partial differential equations: the foam drainage equation and the nonlinear time-fractional fisher’s equation. Through our methods, we aim to provide accurate solutions and gain a deeper understanding of the intricate behaviors exhibited by these systems. Design/methodology/ap...

The article presents a new modification to the modified Extended Direct Algebraic Method (mEDAM) namely r+mEDAM to effectively and precisely acquire propagating soliton and other travelling wave solutions to the Fractional Wazwaz-Benjamin-Bona-Mahony (FWBBM) equation. By using this updated approach, we are able to find more and new families of prop...

This article presents a new approach for solving the fuzzy fractional Degasperis–Procesi (FFDP) and Camassa–Holm equations using the iterative transform method (ITM). The fractional Degasperis–Procesi (DP) and Camassa–Holm equations are extended from the classical DP and Camassa–Holm equations by incorporating fuzzy sets and fractional derivatives....

The main goal of this study is to analyze the nanofluid boundary layer as it flows over a bidirectional, exponentially extending sheet in both convective and magnetic field environments. The mathematical model considers the results of Brownian motion and particle movement caused by a temperature gradient. Using appropriate similarity transformation...

This study demonstrates the use of fractional calculus in the field of epidemiology, specifically in relation to dengue illness. Using noninteger order integrals and derivatives, a novel model is created to examine the impact of temperature on the transmission of the vector–host disease, dengue. A comprehensive strategy is proposed and illustrated,...

This work dives into the Conformable Stochastic Kraenkel-Manna-Merle System (CSKMMS), an important mathematical model for exploring phenomena in ferromagnetic materials. A wide spectrum of stochastic soliton solutions that include hyperbolic, trigonometric and rational functions, is generated using a modified version of Extended Direct Algebraic Me...

In this article, we extend several known results from the ring of all n × n matrices with complex entries to any ring R with nonzero unity 1 and involution *. We introduce various results concerning Hermitian, skew-Hermitian, Unitary and Normal elements of R. Also, we propose two versions of the norm of an element and the orthogonality of two eleme...

The integrable Kuralay-Ⅱ system (K-IIS) plays a significant role in discovering unique complex nonlinear wave phenomena that are particularly useful in optics. This system enhances our understanding of the intricate dynamics involved in wave interactions, solitons, and nonlinear effects in optical phenomena. Using the Riccati modified extended simp...

In this paper, we explore advanced methods for solving partial differential equations (PDEs) and systems of PDEs, particularly those involving fractional-order derivatives. We apply the Mohand transform iterative method (MTIM) and the Mohand residual power series method (MRPSM) to address the complexities associated with fractional-order differenti...

Host (base) fluids are unable to deliver efficient heating and cooling processes in industrial applications due to their limited heat transfer rates. Nanofluids, owing to their distinctive and adaptable thermophysical characteristics, find a widespread range of practical applications in various disciplines of nanotechnology and heat transfer equipm...

In this research, we use the homotopy perturbation method (HPM) combined with the Elzaki transform to investigate the fractional Biswas–Milovic equation (BME) within the framework of the Caputo operator. The fractional BME is a significant mathematical model with applications in various scientific and engineering fields, including physics, biology,...

This study examines the heat transfer properties of a recently created hybrid nanofluid in contrast to a traditional nanofluid. The aim is to improve the transfer of heat in the flow of the boundary layer by employing this novel hybrid nanofluid. Our study investigates the impact of the Lorentz force on a three-dimensional stretched surface. We uti...

In this paper, I utilize the Laplace residual power series method (LRPSM) along with a novel iteration technique to investigate the Fitzhugh-Nagumo equation within the framework of the Caputo operator. The Fitzhugh-Nagumo equation is a fundamental model for describing excitable systems, playing a crucial role in understanding various physiological...

The human immunodeficiency virus, which attacks the immune system and especially targets CD4 cells that are crucial for immunological defense against infections, is the cause of the severe illness known as acquired immunodeficiency syndrome (AIDS). This condition has the potential to take a patient’s life. Understanding the dynamics of AIDS and eva...

Momentum and heat transmission influence the coated physical characteristics of wire product. As a result, understanding the polymeric movement and heat mass distribution is crucial. An increase in thermal efficiency is necessary for the wire covering technology. So, the aim of this work is to investigate the influence of nanomaterials on the heat...

Nanomaterials have found wide applications in many fields, leading to significant interest in the scientific world, in particular automobile thermal control, heat reservoirs, freezers, hybrid control machines, paper creation, cooling organisms, etc. The aim of the present study is to investigate the MHD non-Newtonian nanofluid and time-based stabil...

In this study, we use a dual technique that combines the Laplace residual power series method (LRPSM) and the new iteration method, both of which are combined with the Caputo operator. Our primary goal is to solve two unique but difficult partial differential equations: the foam drainage equation and the nonlinear time-fractional Fisher’s equation....

This paper introduces the optimal auxiliary function method (OAFM) for solving a nonlinear system of Belousov–Zhabotinsky equations. The system is characterized by its complex dynamics and is treated using the Caputo operator and concepts from fractional calculus. The OAFM provides a systematic approach to obtain approximate analytical solutions by...

In this study, we present a comprehensive comparison of two powerful analytical techniques, Aboodh Adomian decomposition method (AADM) and homotopy perturbation transform method (HPTM), for obtaining series solutions of nonlinear partial differential equations, specifically focusing on Camassa–Holm (CH) and Degasperis–Procesi (DP) equations. These...

In this paper, we investigate the fractional-order Klein–Fock–Gordon equations on quantum dynamics using a new iterative method and residual power series method based on the Caputo operator. The fractional-order Klein–Fock–Gordon equation is a generalization of the traditional Klein–Fock–Gordon equation that allows for non-integer orders of differe...

This paper presents a new approach for finding analytic solutions to the Belousov–Zhabotinsky system by combining the Adomian decomposition method (ADM) and the homotopy perturbation method (HPM) with the Elzaki transform. The ADM and HPM are both powerful techniques for solving nonlinear differential equations, and their combination allows for a m...

In this study, we solve the fractional advection–dispersion equation (FADE) by applying the Laplace transform decomposition method (LTDM) and the variational iteration transform method (VITM). The Atangana–Baleanu (AB) sense is used to describe the fractional derivative. This equation is utilized to determine solute transport in groundwater and soi...

This study addresses a nonlinear fractional Drinfeld–Sokolov–Wilson problem in dispersive water waves, which requires appropriate numerical techniques to obtain an approximative solution. The Adomian decomposition approach, the homotopy perturbation method, and Sumudu transform are combined to tackle the problem. The Caputo manner is used to descri...

The q-homotopy analysis transform method (q-HATM) is a powerful tool for solving differential equations. In this study, we apply the q-HATM to compute the numerical solution of the fractional-order Kolmogorov and Rosenau–Hyman models. Fractional-order models are widely used in physics, engineering, and other fields. However, their numerical solutio...

In this study, we implemented the Yang residual power series (YRPS) methodology, a unique analytical treatment method, to estimate the solutions of a non-linear system of fractional partial differential equations. The RPS approach and the Yang transform are togethered in the YRPS method. The suggested approach to handle fractional systems is explai...

This paper introduces a novel numerical approach for tackling the nonlinear fractional Phi-four equation by employing the Homotopy perturbation method (HPM) and the Adomian decomposition method (ADM), augmented by the Shehu transform. These established techniques are adept at addressing nonlinear differential equations. The equation's complexity is...

The current work investigates solitary wave solutions for the fractional modified Degasperis-Procesi equation and the fractional gas dynamics equation with Caputo's derivative by using a modified extended direct algebraic method. This method transforms the targeted fractional partial differential equations (FPDEs) into more manageable nonlinear ord...

The development of numeric-analytic solutions and the construction of fractional-order mathematical models for practical issues are of the greatest importance in a variety of applied mathematics, physics, and engineering problems. The Laplace residual-power-series method (LRPSM), a new and dependable technique for resolving fractional partial diffe...

In this particular research article, we take an analytic function Q 4 L = 1 + 5 / 6 z + 1 / 6 z 5 , which makes a four-leaf-shaped image domain. Using this specific function, two subclasses, S 4 L ∗ and C 4 L , of starlike and convex functions will be defined. For these classes, our aim is to find some sharp bounds of inequalities that consist of l...

With effective techniques like the homotopy perturbation approach and the Adomian decomposition method via the Yang transform, the time-fractional vibration equation's solution is found for large membranes. In Caputo's sense, the fractional derivative is taken. Numerical experiments with various initial conditions are carried out through a few test...

In this article, we solved pantograph delay differential equations by utilizing an efficient numerical technique known as Chebyshev pseudospectral method. In Caputo manner fractional derivatives are taken. These types of problems are reduced to linear or nonlinear algebraic equations using the suggested approach. The proposed method's convergence i...

In this study, we propose a method to study fractional-order shock wave equations and wave equations arising from the motion of gases. The fractional derivative is taken in Caputo manner. The approaches we used are the combined form of the Yang transform (YT) together with the homotopy perturbation method (HPM) called homotopy perturbation Yang tra...

This work combines a ZZ transformation with the Adomian decomposition method to solve the fractional-order Fokker-Planck equations. The fractional derivative is represented in the Atangana-Baleanu derivative. It is looked at with graphs that show that the accurate and estimated results are close to each other, indicating that the method works. Frac...

In this article, we investigate the nonlinear model describing the various physical and chemical phenomena named the Kuramoto–Sivashinsky equation. We implemented the natural decomposition method, a novel technique, mixed with the Caputo–Fabrizio (CF) and Atangana–Baleanu deriavatives in Caputo manner (ABC) fractional derivatives for obtaining the...

This work aims at a new semi-analytical method called the variational iteration transformation method for solving nonlinear homogeneous and nonhomogeneous fractional-order gas dynamics equations. The Shehu transformation and the iterative technique are applied to solve the suggested problems. The proposed method has an advantage over existing appro...

Let G be a group and R be a G-graded ring. In this paper, we present and examine the concept of graded weakly 2-absorbing ideals as in generality of graded weakly prime ideals in a graded ring which is not commutative, and demonstrates that the symmetry is obtained as a lot of the outcomes in commutative graded rings remain in graded rings that are...

For commutative graded rings, the concept of graded $2$-absorbing (graded weakly $2$-absorbing) ideals was introduced and examined by Al-Zoubi, Abu-Dawwas and \c{C}eken (Hacettepe Journal of Mathematics and Statistics, 48 (3) (2019), 724-731) as a generalization of the concept of graded prime (graded weakly prime) ideals. Up to now, research on the...

Let R be a commutative graded ring with unity, S be a multiplicative subset of homogeneous elements of R and P be a graded ideal of R such that P⋂S=∅. In this article, we introduce the concept of graded S-primary ideals which is a generalization of graded primary ideals. We say that P is a graded S-primary ideal of R if there exists s∈S such that f...

In this article, we show how there are strong relations between algebraic properties of a graded commutative ring R and topological properties of open subsets of Zariski topology on the graded prime spectrum of R. We examine some algebraic conditions for open subsets of Zariski topology to become quasi-compact, dense and irreducible. We also presen...

The main goal of this article is to explore the concepts of graded $\phi$-$2$-absorbing and graded $\phi$-$2$-absorbing primary submodules as a new generalization of the concepts of graded $2$-absorbing and graded $2$-absorbing primary submodules. Let $\phi: GS(M)\rightarrow GS(M)\bigcup\{\emptyset\}$ be a function, where $GS(M)$ denotes the collec...

In this article, we consider the structure of graded rings, not necessarily commutative nor with unity, and study the graded weakly prime ideals. We investigate the graded rings in which all graded ideals are graded weakly prime. Several properties are given, and several examples to support given propositions are constructed. We initiate the study...

Let $R$ be a graded commutative ring with non-zero unity $1$ and $M$ be a graded unitary $R$-module. In this article, we introduce the concepts of graded $\phi$-$2$-absorbing and graded $\phi$-$2$-absorbing primary submodules as generalizations of the concepts of graded $2$-absorbing and graded $2$-absorbing primary submodules. Let $GS(M)$ be the s...

Let $R$ be a graded commutative ring with non-zero unity $1$ and $M$ be a graded unitary $R$-module. Let $GS(M)$ be the set of all graded $R$-submodules of $M$ and $\phi: GS(M)\rightarrow GS(M)\bigcup\{\emptyset\}$ be a function. A proper graded $R$-submodule $K$ of $M$ is said to be a graded $\phi-$prime $R$-submodule of $M$ if whenever $r$ is a h...

In this article, we consider the structure of graded rings, not necessarily commutative nor with unity, and study the graded weakly prime ideals. We investigate the graded rings in which all graded ideals are graded weakly prime. Several properties are given, and several examples to support given propositions are constructed. We initiate the study...

In this article, we deal with Zariski topology on graded comultiplication modules. The purpose of this article is to obtain some connections between algebraic properties of graded comultiplication modules and topological properties of dual Zariski topology on graded comultiplication modules.