This manuscript presents several applications for solving special kinds of ordinary and partial differential equations using iteration methods such as Adomian decomposition method (ADM), Variation iterative method (VIM) and Taylor series method. These methods can be applied as well as to solve nonperturbed problems and 3rd order parabolic PDEs with variable coefficient. Moreover, we compare the results using ADM, VIM and Taylor series method. These methods are a commination of the two initial conditions.

In this paper, some necessary and sufficient conditions are obtained to ensure the oscillatory of all solutions of the first order impulsive neutral differential equations. Also, some results in the references have been improved and generalized. New lemmas are established to demonstrate the oscillation property. Special impulsive conditions associated with neutral differential equation are submitted. Some examples are given to illustrate the obtained results.

     A fuzzy valued diffusion term, which in a fuzzy stochastic differential equation refers to one-dimensional Brownian motion, is defined by the meaning of the stochastic integral of a fuzzy process. In this paper, the existence and uniqueness theorem of fuzzy stochastic ordinary differential equations, based on the mean square convergence of the mathematical induction approximations to the associated stochastic integral equation, are stated and demonstrated.

      In this paper, a new class of ordinary differential equations is designed for some functions such as probability density function, cumulative distribution function, survival function and hazard function of power function distribution, these functions are used of the class under the study. The benefit of our work is that the equations ,which are generated from some probability distributions, are used to model and find  the  solutions  of problems in our lives, and that the solutions of these equations are a solution to these problems, as the solutions of the equations under the study are the closest and the most reliable to reality. The existence and uniqueness of solutions the obtained equations in the current study are dis

In this paper , an efficient new procedure is proposed to modify third –order iterative method obtained by Rostom and Fuad [Saeed. R. K. and Khthr. F.W. New third –order iterative method for solving nonlinear equations. J. Appl. Sci .7(2011): 916-921] , using three steps based on Newton equation , finite difference method and linear interpolation. Analysis of convergence is given to show the efficiency and the performance of the new method for solving nonlinear equations. The efficiency of the new method is demonstrated by numerical examples.

In this paper, the author established some new integral conditions for the oscillation of all solutions of nonlinear first order neutral delay differential equations. Examples are inserted to illustrate the results.

This paper is concerned with the oscillation of all solutions of the n-th order delay differential equation . The necessary and sufficient conditions for oscillatory solutions are obtained and other conditions for nonoscillatory solution to converge to zero are established.

This paper deals with the thirteenth order differential equations linear and nonlinear in boundary value problems by using the Modified Adomian Decomposition Method (MADM), the analytical results of the equations have been obtained in terms of convergent series with easily computable components. Two numerical examples results show that this method is a promising and powerful tool for solving this problems.

In this paper, the construction of Hermite wavelets functions and their operational matrix of integration is presented. The Hermite wavelets method is applied to solve nth order Volterra integro diferential equations (VIDE) by expanding the unknown functions, as series in terms of Hermite wavelets with unknown coefficients. Finally, two examples are given