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Research Title :An Efficient Reproducing Kernel Method for Solving Fractional Electro-hydrodynamic Flow Differential Equation

Authors : Banan Maayah, Sana Abu-Ghurra

Abstract :this paper aims to find an approximate numerical solution to the singular nonlinear boundary value problem (BVP) with conformable fractional derivative by using Reproducing kernel method (RKM). The problem contains singularity and strong nonlinear terms; hence, the presented method shows affected and validated results. The (BVP) contains two influential parameters \mathcal{H}^{2} and \eta, therefore we examine the problem for different values of these parameters and their effected of the speed of the fluid. Also, the relation of \mathcal{H}^{2} and \eta together with the speed of the fluid for different values of fractional derivatives

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Research Title :Adaptive Technique for Solving 1-D Interface Problems of Fractional Order The link of publication

Authors :Rahma Al-Masaeed, Banan Maayah & Sana Abu-Ghurra

Abstract :In this paper, we present a numerical technique for solving 1-D interface problems of fractional order. This technique relies on the reproducing kernel functions and the shooting method. The biggest advantage over the existing standard analytical techniques is overcoming the difficulty arising in calculating complicated terms. Numerical examples are inspected to feature the significant highlights of this technique. Moreover, the solution procedure is simple, more effective and clearer

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Research Title :Application of the modified differential transform method to fractional oscillators

Authors :Sana abu-ghurra , Vedat Suat Erturk, Shaher momani

Abstract :Purpose – The purpose of this paper is to find a semi‐analytic solution to the fractional oscillator equations. In this paper, the authors apply the modified differential transform method to find approximate analytical solutions to fractional oscillators. Design/methodology/approach – The modified differential transform method is used to obtain the solutions of the systems. This approach rests on the recently developed modification of the differential transform method. Some examples are given to illustrate the ability and reliability of the modified differential transform method for solving fractional oscillators. Findings – The main conclusion is that the proposed method is a good way for solving such problems. The results are compared with those obtained by the fourth‐order Runge‐Kutta method. It is shown that the results reveal that the modified differential transform method in many instances gives better results. Originality/value – The paper demostrates that a hybrid method of differential transform method, Laplace transform and Padé approximations provides approximate solutions of the oscillatory systems

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Research Title :Numerical Solution of Fuzzy Heat Equation with Complex Dirichlet Conditions

Authors :Hamzeh Husni Zureigat, Abd ULazeez Alkouri,Areen Saber Al-khateeb, Eman abuteen, Sana Abu-Ghurra

Abstract :In this study, complex fuzzy numbers are discussed and applied for the first time to solve a complex fuzzy partial differential equation involving a complex fuzzy heat equation under Hukuhara differentiability. Subsequently, an explicit finite difference scheme, referred to as the forward time-center space (FTCS), was implemented to solve the complex fuzzy heat equations. The imprecision of the issue is evident in the initial and boundary conditions, as well as in the amplitude and phase terms’ coefficients, where the convex normalized triangular fuzzy numbers are extended to the unit disk in the complex plane. The proposed numerical methods utilized the properties and benefits of the complex fuzzy set theory. Furthermore, a new proof of consistency, stability, and convergence was established under this theory. A numerical example was provided to illustrate the reliability and feasibility of the proposed approach. The results obtained using the proposed approach are in adequate agreement with the exact solution and related theoretical aspects

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Research Title :Similarity solution of heat transfer for the upper-convected maxwell casson fluid over a stretching/shrinking sheet with thermal radiation

Authors : Dr: Hamzeh Taha Alkasasbeh , Sana Abu-Ghurra, Husein A. Alzgool

Abstract :The heat transfer for the upper-convected Maxwell Casson fluid over a stretching/shrinking sheet with thermal radiation is studied. With the help of similarity transformations, the governing equations are converted into nonlinear system of ordinary differential equations. Runge Kutta Fehlberg fourth-fifth order (RKF45) method is employed to obtain the numerical solutions for the skin friction coefficient, heat transfer coefficient, and velocity and temperature. The effects of various parameters such as the Casson parameter, Maxwell parameter, the radiation parameter, the suction parameter and the stretching and shrinking parameter are considered as distributions. Closed form analytic solutions are also obtained. The results obtained under the special cases are illustrated graphically and compared with previous results to support their validity

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Research Title :Numerical Solution of Heat Transfer in MHD Mixed Convection Flow Micropolar Casson Fluid about Solid Sphere with Radiation Effect

Authors :Husein A. Alzgool, Hamzeh Taha Alkasasbeh , Sana Abu-Ghurra , Mohammad zaki al Swalmeh

Abstract :This study is conducted to develop a numerical solution of heat transfer in magneto-hydrodynamic mixed convection flow micropolar Casson fluid about solid sphere. The radiation effects are also considered in the energy equation. The governing momentum energy and angular momentum equations are transformed into nonlinear partial differential equations by the use of a non-similarity transformation. These equations are solved numerically subject to an appropriate physical boundary conditions using an implicit finite difference scheme known as the Keller-box method. Several parameters namely the mixed convection parameter ,  Casson fluid parameter ,  magnetic parameter , M radiation parameter R and micropolar parameter K have been involved in the problem. The effect of these parameters on the local Nusselt number and on the local skin friction coefficient, as well as on the temperature, velocity and angular velocity profiles are illustrated graphically. The obtained results are validated with previously published available results and are found to be in good agreement

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Research Title :An Approximation of the Analytic Solution of the Helmholtz Equation

Authors :Shaher Mohammad Momani, Vedat Suat Erturk , Sana Abu-Ghurra

Abstract :In this article we discuss the analytic solution of the linear Helmholtz partial differential equation. The analytic solution is obtained by using differential transform method. Some numerical examples are presented to illustrate the efficiency and reliability of the method