Maha Sa’da Abed Alsoudi

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Maha Sa’da Abed Alsoudi

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Research

Research Title :1New algebraic approach towards interval-valued neutrosophic cubic vague set based on subbisemiring over bisemiring

Authors : S. Selvaraj1, Gharib Gharib2, Abdallah Al-Husban3, Maha Al Soudi4, K. Lenin Muthu Kumaran5 , Murugan Palanikumar6, K. Sundareswari7

Abstract :ABSTRACTWe introduce the concept of an interval-valued neutrosophic cubic vague subbisemiring (IVNCVSBS) and level set of IVNCVSBS of a bisemiring. An IVNCVSBS is the new extension of neutrosophic subbisemirings andSBSoverbisemirings. Let beaneutrosophicvaguesubsetin ,weshowthat = ([ + ] [ + ] [ is a IVNCVSBS of ifand only if all non empty level set ( 1 2 s) is a SBS of for all 1 2 s [01]. Let be the IVNCVSBS of and be the strongest cubic neutrosophic vague relation of . To prove that is a IVNCVSBS of . Let be any IVNCVSBS of , prove that pseudo cubic neutrosophic vague coset ( )pisaIVNCVSBSof ,forall . Let 1 2 respectively. To prove that 1 2 n bethe family of IV NCVSBSs of 1 2 n is a IVNCVSBSof 1 2 n . The homomorphic image of every IVNCVSBS is a IVNCVSBS. The homomorphic pre-image of every IVNCVSBS is a IVNCVSBS. Examples are provided to strengthen our results.

Keywords : Subbisemiring; cubic neutrosophic subbisemiring; vague bisemiring; homomorphism

Research Title :2-Conformable Triple Sumudu Transform with Applications

Authors :GHARIB M. GHARIB1, MAHA S. ALSAUODI2, MOHAMAD ABU-SEILEEK

Abstract :One of the important topics in applied mathematics is the topic of integral transformations, due to their importance in electrical engineering applications, including communications in particular, and other sciences. In this work, one of the most important transformations in its three dimensions was presented, which is the triple Sumudu transform, including solving some real-life applications of physics, some of which have not been solved using such an integral transform before. In this work, we extend the Sumudu transform formula to the conformable fractional order, as well as other interesting and significant rules. The general analytical solution of a singular and nonlinear conformable fractional differential equation based on the conformable fractional Sumudu transform is also presented in this paper. The general solutions of several linear and nonhomogeneous conformable fractional differential equations can be obtained using the method we've proposed. As a result, our results reveal that our proposed method is an efficient one that can be used for solving all conformable fractional differential equations. The relationship between the Sumudu integral transform and other important and recently proposed integral transforms are also discussed. Finally, the triple Sumudu transform is used to solve boundary value problems, such as the heat equation with boundary values. The triple Sumudu integral transform is also used to solve linear partial integro-differential equations. The transform capability to handle such equations has been proven via its utilization in three applications.

Keywords : : Triple Sumudu Transform; Sumudu Transform, Partial differential equation, Integral equation. Transform, Double Transform, partial integro-differential equations, fractional Sumudu transform , fractional equation.

Research Title :3-On Stability of a Fractional Discrete Reaction–Diffusion Epidemic Model

Authors :OmarAlsayyed 1 ,AmelHioual2,* , Gharib M. Gharib 3, Mayada Abualhomos 4, Hassan Al-Tarawneh 5, MahaS. Alsauodi 6, Nabeela Abu-Alkishik 7, Abdallah Al-Husban 8 and Adel Ouannas 9

Abstract :This paper considers the dynamical properties of a space and time discrete fractional reaction–diffusion epidemic model, introducing a novel generalized incidence rate. The linear stability of the equilibrium solutions of the considered discrete fractional reaction–diffusion mode has been carried out, and a global asymptotic stability analysis has been undertaken. We conducted a global stability analysis using a specialized Lyapunov function that captures the system’s historical data, distinguishing it from the integer-order version. This approach significantly advanced our comprehension of the complex stability properties within discrete fractional reaction–diffusion epidemic models. To substantiate the theoretical underpinnings, this paper is accompanied by numerical examples. These examples serve a dual purpose: not only do they validate the theoretical f indings, but they also provide illustrations of the practical implications of the proposed discrete fractional system

Keywords :fractional discrete epidemic reaction–diffusion model; local stability; Lyapunov function; global stability

Research Title :4-Bifurcation, Hidden Chaos, Entropy and Control in Hénon-Based Fractional Memristor Map with Commensurate and Incommensurate Orders

Authors :Mayada Abualhomos 1, Abderrahmane Abbes 2,*, Gharib Mousa Gharib 3, Abdallah Shihadeh 4 , MahaS. AlSoudi 5, AhmedAtallah Alsaraireh 6 and Adel Ouannas 7

Abstract :In this paper, we present an innovative 3D fractional Hénon-based memristor map and conduct an extensive exploration and analysis of its dynamic behaviors under commensurate and incommensurate orders. The study employs diverse numerical techniques, such as visualizing phase portraits, analyzing Lyapunov exponents, plotting bifurcation diagrams, and applying the sample entropy test to assess the complexity and validate the chaotic characteristics. However, since the proposed fractional map has no fixed points, the outcomes reveal that the map can exhibit a wide range of hidden dynamical behaviors. This phenomenon significantly augments the complexity of the fractal structure inherent to the chaotic attractors. Moreover, we introduce nonlinear controllers designed for stabilizing and synchronizing the proposed fractional Hénon-based memristor map. The research emphasizes the system’s sensitivity to fractional-order parameters, resulting in the emergence of distinct dynamic patterns. The memristor-based chaotic map exhibits rich and intricate behavior, making it a captivating and significant area of investigation.

Keywords :Hénon-based map; memristor; discrete fractional calculus; chaotic dynamics; entropy; control.

Research Title :5-On Chaos and Complexity Analysis for a New Sine-Based Memristor Map with Commensurate and Incommensurate Fractional Orders

Authors :Tareq Hamadneh 1, Abderrahmane Abbes 2,* , Hassan Al-Tarawneh 3, Gharib Mousa Gharib 4, Wael MahmoudMohammadSalameh5 , Maha S. Al Soudi 6 and Adel Ouannas 7

Abstract :In this study, we expanda2Dsinemapviaaddingthediscretememristortointroduceanew 3Dfractional-order sine-based memristor map. Under commensurate and incommensurate orders, we conduct an extensive exploration and analysis of its nonlinear dynamic behaviors, employing diverse numerical techniques, such as analyzing Lyapunov exponents, visualizing phase portraits, and plotting bifurcation diagrams. The results emphasize the sine-based memristor map’s sensitivity to fractional-order parameters, resulting in the emergence of distinct and diverse dynamic patterns. In addition, we employ the sample entropy (SampEn) method and C0 complexity to quantitatively measure complexity, and we also utilize the 0–1 test to validate the presence of chaos in the proposed fractional-order sine-based memristor map. Finally, MATLAB simulations are be executed to confirm the results provided.

Keywords :chaos; sine memristor map; discrete fractional calculus; complexit

Research Title :6-The New Four-Dimensional Fractional Chaotic Map with Constant and Variable-Order: Chaos, Control and Synchronization

Authors : Tareq Hamadneh 1, Souad Bensid Ahmed 2, Hassan Al-Tarawneh 3, Omar Alsayyed 4 , Gharib Mousa Gharib 5, MahaS. AlSoudi 6, Abderrahmane Abbes 7,* and Adel Ouannas 8

Abstract :ABSTRACTUsing fractional difference equations to describe fractional and variable-order maps, this manuscript discusses the dynamics of the discrete 4D sinusoidal feedback sine iterative chaotic map with infinite collapse (ICMIC) modulation map (SF-SIMM) with fractional-order. Also, it presents a novel variable-order version of SF-SIMM and discusses their chaotic dynamic behavior by employing a distinct function for the variable fractional-order. To establish the existence of chaos in the suggested discrete SF-SIMM, some numerical methods such as phase plots, bifurcation and largest Lyapunov exponent diagrams, C0 complexity and 0–1 test are utilized. After that, two different control schemes are used for the conceived discrete system. The states are stabilized and asymptotically forced towards zero by the first controller. The second controller is used to synchronize a pair of maps with non–identical parameters. Finally, MATLAB simulations will be executed to confirm the results provided

Keywords :variable fractional-order; dynamical behavior; chaos; C0 complexity; largest Lyapunov exponents.

Research Title :7-Novel Approach to Multi-Criteria Decision-Making Based on the n,mPR-Fuzzy Weighted Power Average Operator

Authors :Tareq Hamadneh 1, Hariwan Z. Ibrahim 2,* , Mayada Abualhomos 3, Maha Mohammed Saeed 4 Gharib Gharib 5, Maha Al Soudi 6 and Abdallah Al-Husban 7

Abstract :significant addition to fuzzy set theory for expressing uncertain data is an n,m-th power root fuzzy set. Compared to the nth power root, Fermatean, Pythagorean, and intuitionistic fuzzy sets, n,m-th power root fuzzy sets can cover more uncertain situations due to their greater range of displayed membership grades. When discussing the symmetry between two or more objects, the innovative concept of an n,m-th power root fuzzy set over dual universes is more flexible than the current notion of an intuitionistic fuzzy set, a Pythagorean fuzzy set, and a nth power root fuzzy set. In this study, we demonstrate a number of additional operations on n,m-th power root fuzzy sets along with a number of their special aspects. Additionally, to deal with choice information, we create a novel weighted aggregated operator called the n,m-th power root fuzzy weighted power average (FWPAnm) across n,m-th power root fuzzy sets and demonstrate some of its fundamental features. To rank n,m-th power root fuzzy sets, we also define the score and accuracy functions. Moreover, we use this operator to identify the countries with the best standards of living and show how we can select the best option by contrasting aggregate results using score values. Finally, we contrast the results of the FWPAnm operator with the square-root fuzzy weighted power average (SR-FWPA), the nth power root fuzzy weighted power average (nPR-FWPA), the Fermatean fuzzy weighted power average (FFWPA), and the n,m-rung orthopair fuzzy weighted power average (n,m-ROFWPA) operators.

Keywords : n,mPR-fuzzy sets; operations; score function; aggregation operator

Research Title :8-New Two Parameter Integral Transform “MAHA Transform” and its Applications in Real Life.

Authors : MAHA ALSAOUDI1, GHARIB GHARIB2, EMAD KUFFI3, AHLAM GUIATNI4*

Abstract :In this paper, an integral transform with two parameters was proposed, and this transform was applied to obtain the exact solutions for the linear ordinary differential equations with constant coefficients of higher orders. This integral transform was also applied and we called it Maha transform in nuclear physics and for medical applications.

Keywords : MAHA transform, Inverse MAHA transform, Integral transform, Ordinary differential equations, coefficients of higher orders, Integral transform for two parameters.

Research Title :9-Steps of Exact and Analytic Solutions of Ordinary Differential Equations using MAHA Integral Transform and Its Applications.

Authors : MAHA ALSAOUDI1, AHMAD SHARIEH2, AHLAM GUIATNI3,*, GHARIB GHARIB4

Abstract :Transformation such as integral transform is needed to obtain the exact solutions for linear ordinary differential equations (ODEs) with constant coefficients of higher orders. MAHA transformation exact solution of ODEs is simpler and easier than the previous with two parameters. The major steps of this transform are applying the MAHA transform on the given equation followed by taking the inverse transform. The general steps in numerical solutions involve defining the ODE as a function, defining initial conditions and the range of the independent variable, using an appropriate ODE solver function, and calling the solver and plotting the solution using a programming language. The exact and analytical solutions are validated. Both methods are easy and simple to be deployed in computing scientific applications such as nuclear physics and medical applications.

Keywords :MAHA transform, Integral transform of two parameters, Inverse of MAHA transform, Medical Applications, Nuclear Physics, Ordinary differential equations.

Research Title :10- On Ikeda-Based Memristor Map with Commensurate and Incommensurate Fractional Orders: Bifurcation, Chaos, and Entropy

Authors : Omar Alsayyed 1 ,Abderrahmane Abbes 2,*,Gharib Mousa Gharib 3,Mayada Abualhomos 4,Hassan Al-Tarawneh 5,Maha S. Al Soudi 6,Nabeela Abu-Alkishik 7,Abdallah Al-Husban 8 andAdel Ouannas

Abstract :This paper introduces a novel fractional Ikeda-based memristor map and investigates its non-linear dynamics under commensurate and incommensurate orders using various numerical techniques, including Lyapunov exponent analysis, phase portraits, and bifurcation diagrams. The results reveal diverse and complex system behaviors arising from the interplay of different fractional orders in the proposed map. Furthermore, the study employs the sample entropy test to quantify complexity and validate the presence of chaos. Non-linear controllers are also presented to stabilize and synchronize the model. The research emphasizes the system’s sensitivity to the fractional order parameters, leading to distinct dynamic patterns and stability regimes. The memristor-based chaotic map exhibits rich and intricate behavior, making it an interesting and important area of research.

Keywords : Ikeda-based memristor map; discrete fractional calculus; bifurcation; chaotic dynamics; sample entropy; control

Research Title :11- A Generalization of Gegenbauer Polynomials and Bi-Univalent Functions

Authors : Ala Amourah 1,* , Abdullah Alsoboh 2,* , Osama Ogilat 3 and MahaAlSoudi5 1 , Gharib Mousa Gharib 4 , Rania Saadeh 4

Abstract :Three subclasses of analytic and bi-univalent functions are introduced through the use of q Gegenbauer polynomials, which are a generalization of Gegenbauer polynomials. For functions falling within these subclasses, coefficient bounds a2 and a3 as well as Fekete–Szegö inequalities are derived. Specializing the parameters used in our main results leads to a number of new results

Keywords :Fekete–Szegö problem; q–Gegenbauer polynomials; bi-univalent functions; q–calculus; analytic function

Research Title :12- Solving Non Linear Fractional Newell-Whitehead Equation By Atomic Solution

Authors : GHARIB GHARIB1 , MAHA ALSOUDI2, IBTISSEM BENKEMACHE3

Abstract :Abstract: Sometimes, it is not possible to find a general solution for some differential equations using some classical methods, like separation of variables. In such a case, one can try to use theory of tensor product of Banach spaces to find certain solutions, called atomic solutions. The goal of this paper is to find atomic solution for Fractional Newell- Witehead type equation.

Keywords : Conformable derivative, tensor product, atomic solution.

Research Title :13- Using Modified Atomic Solution Method to Solve Nonhomogeneous Fractional

Authors : Gharib M. Gharib, Maha S. Alsauodi, Rania Saadeh, Worood A. AL-hakim & Bara’a A. Abujarad

Abstract :In this work, one of the top new method called “Atomic Solution” that used to solve some partial fractional deferential equations that contains tensor product and variables from Banach space. This method is then used to solve the Fractional PDE Equation step by step, in order to illustrate the effectiveness of the method.

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Research Title :14-A COMMONFIXED POINT THEOREM IN AN M-METRIC SPACE AND AN APPLICATION

Authors :Gharib M. Gharib1, Abed Al-Rahman M. Malkawi2, Ayat M. Rabaiah3, Was A. Shatanawi4, Maha S. Alsauodi5

Abstract :In this paper, we introduce the concept of M-metric spaces and how much the M-metric and the b-metric spaces are related. Moreover, we introduce some ways of generating M-metric spaces. Also, we investigate some types of convergence associated with M-metric spaces. Some common xed point for contraction and generalized contraction mappings in M-metric spaces. Our work has been supported by many examples and an application

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Research Title :15- Solutions of Certain Fractional Partial Differential Equations

Authors : ALSAUODIMAHA ALHORANIMOHAMMED KHALIL ROSHDI ABSTRACT

Abstract :Abstract: In this paper we find certain solutions of some fractional partial differential equations. Tensor product of Banach spaces is used where separation of variables doesnot work

Keywords :Conformable derivative, Tensor product, fractional Laplace type equation

Research Title :16-Fixed point theorems for monotone mappings on partial M * -metric spaces

Authors : Maha S Alsauodi Gharib Mousa Gharib Abed Al-Rahman Mohammad Malkawi Ayat M Rabaiah Wasfi Shatanawi

Abstract :In this paper, we introduce the concept of partial M * −metric on a nonempty set X, and we give some properties supported by some examples to illustrate *. Corresponding author FIXED POINT THEOREMS FOR MONOTONE MAPPINGS ON PARTIAL ... 155 our results. Furthermore, we establish some fixed points results for partial M * −metric. Also, we extend our result for monotone mappings on partial M * −metric spaces

Keywords : M∗−metric spaces, fixed point, partial metric

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