Shaher Momani | The University Of Jordan (original) (raw)

Shaher Momani

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Papers by Shaher Momani

In this paper, we develop and analyze the use of the Optimal Homotopy Asymptotic Method (OHAM) to... more In this paper, we develop and analyze the use of the Optimal Homotopy Asymptotic Method (OHAM) to find the approximate analytical solution for partial differential equation involving fuzzy heat equation. OHAM allows the solution of the partial differential equation to be calculated in the form of an infinite series in which the components can be easily computed. The convergence theorem of this method in fuzzy case is presented and proved. This method provides us with a convenient way to control the convergence of approximation series. The method is tested on linear fuzzy heat equations and comparing the exact solution that were made with numerical results showed the effectiveness and accuracy of this method.

In this paper, the continuous genetic algorithm is applied for the solution of singular two-point... more In this paper, the continuous genetic algorithm is applied for the solution of singular two-point boundary value problems, where smooth solution curves are used throughout the evolution of the algorithm to obtain the required nodal values. The proposed technique might be considered as a variation of the finite difference method in the sense that each of the derivatives is replaced by an appropriate difference quotient approximation.

Hindawi Publishing Corporation, 2012

This paper investigates the numerical solution of nonlinear Fredholm-Volterra integro-differentia... more This paper investigates the numerical solution of nonlinear Fredholm-Volterra integro-differential equations using reproducing kernel Hilbert space method. The solution 𝑢 (𝑥) is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximate solution 𝑢𝑛 (𝑥) is obtained and it is proved to converge to the exact solution 𝑢 (𝑥).

$Research paper thumbnail of Existence of the mild solution for fractional semilinear initial value problems$

Nonlinear Analysis-theory Methods & Applications, 2008

... Article Outline. 1. Introduction 2. The main theorems References. ... 2. The main theorems. I... more ... Article Outline. 1. Introduction 2. The main theorems References. ... 2. The main theorems. In this section, we shall prove our main results, we begin by proving a theorem concerned with the existence and uniqueness of mild solution for the semilinear initial value problem (1). ...

$Research paper thumbnail of Application of homotopy-perturbation method to fractional IVPs$

Journal of Computational and Applied Mathematics, 2008

$Research paper thumbnail of Homotopy analysis method for fractional IVPs$

Communications in Nonlinear Science and Numerical Simulation, 2009

$Research paper thumbnail of Non-perturbative analytical solutions of the space- and time-fractional Burgers equations$

Chaos Solitons & Fractals, 2006

(1.1) View the MathML source where ε, ν, η are parameters and α and β are parameters describing t... more (1.1) View the MathML source where ε, ν, η are parameters and α and β are parameters describing the order of the fractional time-and space-derivatives, respectively. The function u(x, t) is assumed to be a causal function of time and space, ie, vanishing for t &lt; 0 and x &lt; 0. The fractional ...

$Research paper thumbnail of Analytic and approximate solutions of the space- and time-fractional telegraph equations$

Applied Mathematics and Computation, 2005

$Research paper thumbnail of An explicit and numerical solutions of the fractional KdV equation$

Mathematics and Computers in Simulation, 2005

$Research paper thumbnail of An approximate solution for a fractional diffusion-wave equation using the decomposition method$

Applied Mathematics and Computation, 2005

$Research paper thumbnail of Numerical solutions for systems of fractional differential equations by the decomposition method$

Applied Mathematics and Computation, 2005

$Research paper thumbnail of A novel method for nonlinear fractional partial differential equations: Combination of DTM and generalized Taylor's formula$

Journal of Computational and Applied Mathematics, 2008

Chaos Solitons & Fractals, 2006

$Research paper thumbnail of Solving fractional diffusion and wave equations by modified homotopy perturbation method$

$Research paper thumbnail of Homotopy perturbation method for nonlinear partial differential equations of fractional order$

Physics Letters A, 2007

The aim of this Letter is to present an efficient and reliable treatment of the homotopy perturba... more The aim of this Letter is to present an efficient and reliable treatment of the homotopy perturbation method (HPM) for nonlinear partial differential equations with fractional time derivative. The fractional derivative is described in the Caputo sense. The modified ...

$Research paper thumbnail of Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order$