A theoretical study was done in this work for Fatigue , Fatigue Crack Growth (FCG) and stress factor intensity range for steel .       It also includes Generalized Paris Equation and the fulfillment of his equation which promises that there is a relation between parameters C and n .          Usig Simple Paris Equation through which we concluded the practical values of C and n and compared them with the theoretical values which have been concluded by Generalized Paris Equation .           The value of da/dN and ∆K for every material and sample were concluded and compared with the data which was used in

In this paper, we consider a new approach to solve type of partial differential equation by using coupled Laplace transformation with decomposition method to find the exact solution for non–linear non–homogenous equation with initial conditions. The reliability for suggested approach illustrated by solving model equations such as second order linear and nonlinear Klein–Gordon equation. The application results show the efficiency and ability for suggested approach.

The main objective and primary concern to every investor not only to achieve a greater return on his or her investments, but also to create the largest possible value of these investments the, researchers and those interested in the field of investment and financial analysis  try to develop standards  for performance      valuation      is guided through the                                     &nbsp

Volterra – Fredholm integral equations (VFIEs) have a massive interest from researchers recently. The current study suggests a collocation method for the mixed Volterra - Fredholm integral equations (MVFIEs)."A point interpolation collocation method is considered by combining the radial and polynomial basis functions using collocation points". The main purpose of the radial and polynomial basis functions is to overcome the singularity that could associate with the collocation methods. The obtained interpolation function passes through all Scattered Point in a domain and therefore, the Delta function property is the shape of the functions. The exact solution of selective solutions was compared with the results obtained

In this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal meth