Fadi Awawdeh

Some Fixed Point Theorem for Mapping on Complete G-Metric Spaces

We prove some fixed point results for mapping satisfying sufficient conditions on complete -metric space, also we showed that if the -metric space is symmetric, then the existence and uniqueness of these fixed point results follow from well-known theorems in usual metric space , where is the usual metric space which defined from the -metric space .

On new iterative method for solving systems of nonlinear equations

Solving systems of nonlinear equations is a relatively complicated problem for which a number of different approaches have been proposed. In this paper, we employ the Homotopy Analysis Method (HAM) to derive a family of iterative methods for solving systems of nonlinear algebraic equations. Our approach yields second and third order iterative methods which are more efficient than their classical counterparts such as Newton’s, Chebychev’s and Halley’s methods.

Some fixed and coincidence point theorems for expansive maps in cone metric spaces

In this article, we establish some common fixed and common coincidence point theorems for expansive type mappings in the setting of cone metric spaces. Our results extend some known results in metric spaces to cone metric spaces. Also, we introduce some examples the support the validity of our results.Mathematics Subject Classification: 54H25; 47H10; 54E50.

A New Simplified Bilinear Method for the N-Soliton Solutions for a Generalized FmKdV Equation with Time-Dependent Variable Coefficients

Abstract In this paper a generalized fractional modified Korteweg–de Vries (FmKdV) equation with time-dependent variable coefficients, which is a generalized model in nonlinear lattice, plasma physics and ocean dynamics, is investigated. With the aid of a simplified bilinear method, fractional transforms and symbolic computation, the corresponding N-soliton solutions are given and illustrated. The characteristic line method and graphical analysis are applied to discuss the solitonic propagation and collision, including the bidirectional solitons and elastic interactions. Finally, the resonance phenomenon for the equation is examined.

Symbolic Computation on Soliton Solutions for Variable-coefficient Quantum Zakharov-Kuznetsov Equation in Magnetized Dense Plasmas

Abstract The (3+1)-dimensional quantum Zakharov-Kuznetsov equations with variable coefficients have the applications to nonlinear ion-acoustic waves in dense magnetoplasmas. Via a simplified bilinear method and symbolic computation, we construct the multiple solitary wave solutions, analyze the elastic collisions with the constant and variable coefficients, and observe that solitons no longer keep rectilinear propagation and display different shapes because of the inhomogeneities of media. Then, a dense magnetoplasma consisting of electrons and singly charged ions is considered. The basic set of quantum hydrodynamic is reduced to the quantum Zakharov-Kuznetsov equation by using the reductive perturbation technique. Parametric analysis is carried out in order to illustrate that the soliton amplitude, width and velocity are affected by the quantum diffraction and obliqueness effect. Furthermore, propagation characteristics and interaction behaviors of the solitons are also discussed through the graphical analysis and the characteristic-line method.

Multiple solutions for fractional differential equations: Analytic approach

Multiple solutions of the fractional differential equations is an interesting subject in the area of mathematics, sciences and engineering. A new Algorithm for finding multiple solution of fractional differential equations is constructed based on a homotopy map between initial approximation and exact solution with predictor force condition. Easy and efficient algorithm is introduced to approximate the multiple solutions, even if these multiple solutions are very close and thus rather difficult to distinct even by numerical techniques. Several examples are presented to demonstrate the efficiency of the algorithm. To the best of our knowledge, we present multiple solutions for fractional differential equations analytically.

New exact solitary wave solutions of the Zakharov–Kuznetsov equation in the electron–positron–ion plasmas

Abstract In this paper, the Zakharov–Kuznetsov equation which describes the propagation of the electrostatic excitations in the electron–positron–ion (e–p–i) plasmas are investigated. New exact solitary wave solutions are obtained using Hirota’s bilinear method and generalized three-wave type of ansatz approach. These new exact solutions will enrich previous results and help us further understand the physical structures and analyze the dynamics of the electrostatic solitons in the e–p–i plasmas. Parametric analysis is carried out in order to illustrate that the soliton amplitude, width and velocity are affected by phase velocity, ion-to-electron density ratio, rotation frequency and cyclotron frequency.

Analytic Solution of Multipantograph Equation

We apply the homotopy analysis method (HAM) for solving the multipantograph equation. The analytical results have been obtained in terms of convergent series with easily computable components. Several examples are given to illustrate the efficiency and implementation of the homotopy analysis method. Comparisons are made to confirm the reliability of the homotopy analysis method.

A new approach for the solution of the electrostatic potential differential equations.

This paper is focused on deriving an explicit analytical solution for the prediction of the electrostatic potential, commonly used on electrokinetic research and its related applications. Different from all other analytic techniques, this approach provides a simple way to ensure the convergence of series of solution so that one can always get accurate enough approximations. This new approach can be a useful tool in electrical field applications such as the separation of a mixture of macromolecules and the removal of contaminants in soil cleaning processes.

An Analytical Scheme for Multi-order Fractional Differential Equations

In this work, on the basis of homotopy analysis method, we propose a numerical procedure for solving multi-order fractional differential equations by transforming the original multi-order fractional differential equation into a system of single-order equations. To our knowledge this paper presents the first viable numerical method for an analytic solution of multi-order fractional differential equations. This approach provides a simple way to ensure the convergence of series of solution so that one can always get accurate enough approximations.