Theory of Approximation and Applications
Volume:11 Issue: 1, Winter and Spring 2016

Here, a new method called Aboodh transform homotopy perturbation method (ATHPM) is used to solve nonlinear partial di erential equations, we present a reliable combination of homotopy perturbation method and Aboodh transform to investigate some nonlinear partial di erential equations. The nonlinear terms can be handled by the use of homotopy perturbation method. The results show the eciency of this method. Aboodh transform was introduced by Khalid Aboodh to facilitate the process of solving ordinary and partial di erential equations in the time domain.

In this paper, we investigate the existence of positive solutions for the elliptic equation $\Delta^{2}\,u(x)u = \lambda f(u)$ on a bounded smooth domain $\Omega$ of $\R^{n}$, $n\geq2$, with Navier boundary conditions. We show that there exists an extremal parameter $\lambda^{\ast}>0$ such that for $\lambda \lambda^{\ast}$, the problem has no solution even in the week sense. We also show that $\lambda^{\ast}=\frac{\lambda_{1}}{a}$ if $ \lim_{t\rightarrow \infty}f(t)-at=l\geq0$ and for $\lambda

In this paper a numerical method for solving forth order fuzzy di erential equations under generalized differentiability is proposed. This method is based on the interpolating a solution by piecewise polynomial of degree 8 in the range of solution . We investigate the existence and uniqueness of solutions. Finally a numerical example is presented to illustrate the accuracy of the new technique.

Let H be an infinite--dimensional Hilbert space and K(H) be the set of all compact operators on H. We will adopt spectral theorem for compact self-adjoint operators, to investigate of higher derivation and higher Jordan derivation on K(H) associated with the following cauchy-Jencen type functional equation 2f(\frac{T}{2})=f(T)(S)(R) for all T,S,R\in K(H).

In this paper we obtain a necessary and a sufficient condition for the set of ω_0-nearest points ( ω_0-farthest points) to be non-empty or a singleton set in normed linear spaces. We shall find a necessary and a sufficient condition for an uniquely remotal set to be a singleton set.

In this paper we introduce and investigate a certain subclass of univalent functions which are analytic in the unit disk U.Such results as coecient inequalities. The results presented here would provide extensions of those given in earlier works.

In this paper, based on sinh-cosh method and sinh-Gordon expansion method, families of solutions of (2)-dimensional breaking soliton equation are obtained. These solutions include Jacobi elliptic function solution, soliton solution, trigonometric function solution.