<p>Daftardar Gejji and Hossein Jafari have proposed a new iterative method for solving many of the linear and nonlinear equations namely (DJM). This method proved already the effectiveness in solved many of the ordinary differential equations, partial differential equations and integral equations. The main aim from this paper is to propose the Daftardar-Jafari method (DJM) to solve the Duffing equations and to find the exact solution and numerical solutions. The proposed (DJM) is very effective and reliable, and the solution is obtained in the series form with easily computed components. The software used for the calculations in this study was MATHEMATICA^® 9.0.</p>

The goal of this paper is to design a robust controller for controlling a pendulum
system. The control of nonlinear systems is a common problem that is facing the researchers in control systems design. The Sliding Mode Controller (SMC) is the best solution for controlling a nonlinear system. The classical SMC consists from two phases. The first phase is the reaching phase and the second is the sliding phase. The SMC suffers from the chattering phenomenon which is considered as a severe problem and undesirable property. It is a zigzag motion along the switching surface. In this paper, the chattering is reduced by using a saturation function instead of sign function. In spite of SMC is a good method for controlling a nonlinear system b

In this paper, the series solutions of a non-linear delay integral equations are considered by a modified approach of homotopy analysis method (MAHAM). We split the function   into infinite sums. The outcomes of the illustrated examples are included to confirm the accuracy and efficiency of the MAHAM. The exact solution can be obtained using special values of the convergence parameter.

A numerical algorithm for solving linear and non-linear fractional differential equations is proposed based on the Bees algorithm and Chebyshev polynomials. The proposed algorithm was applied to a set of numerical examples. Faster results are obtained compared to the wavelet methods.

The main objective of this research is to use the methods of calculus ???????? solving integral equations Altbataah When McCann slowdown is a function of time as the integral equation used in this research is a kind of Volterra

The author obtain results on the asymptotic behavior of the nonoscillatory solutions of first order nonlinear neutral differential equations. Keywords. Neutral differential equations, Oscillatory and Nonoscillatory solutions.

The aim of this paper is to propose an efficient three steps iterative method for finding the zeros of the nonlinear equation f(x)=0 . Starting with a suitably chosen , the method generates a sequence of iterates converging to the root. The convergence analysis is proved to establish its five order of convergence. Several examples are given to illustrate the efficiency of the proposed new method and its comparison with other methods.

In this paper, the series solution is applied to solve third order fuzzy differential equations with a fuzzy initial value. The proposed method applies Taylor expansion in solving the system and the approximate solution of the problem which is calculated in the form of a rapid convergent series; some definitions and theorems are reviewed as a basis in solving fuzzy differential equations. An example is applied to illustrate the proposed technical accuracy. Also, a comparison between the obtained results is made, in addition to the application of the crisp solution, when the-level equals one.