In this work, the fractional damped Burger's equation (FDBE) formula    = 0,

The aerodynamic characteristics of general three-dimensional rectangular wings are considered using non-linear interaction between two-dimensional viscous-inviscid panel method and vortex ring method. The potential flow of a two-dimensional airfoil by the pioneering Hess & Smith method was used with viscous laminar, transition and turbulent boundary layer to solve flow about complex configuration of airfoils including stalling effect. Viterna method was used to extend the aerodynamic characteristics of the specified airfoil to high angles of attacks. A modified vortex ring method was used to find the circulation values along span wise direction of the wing and then interacted with sectional circulation obtained by Kutta-Joukowsky theorem of

This paper investigates some exact and local search methods to solve the traveling salesman problem. The Branch and Bound technique (BABT) is proposed, as an exact method, with two models. In addition, the classical Genetic Algorithm (GA) and Simulated Annealing (SA) are discussed and applied as local search methods. To improve the performance of GA we propose two kinds of improvements for GA; the first is called improved GA (IGA) and the second is Hybrid GA (HGA).

The IGA gives best results than GA and SA, while the HGA is the best local search method for all within a reasonable time for 5 ≤ n ≤ 2000, where n is the number of visited cities. An effective method of reducing the size of the TSP matrix was proposed with

  Many production companies suffers from big losses because of  high production cost and low profits for several reasons, including raw materials high prices and no taxes impose on imported goods also consumer protection law deactivation and national product and customs law, so most of consumers buy imported goods because it is characterized by modern specifications and low prices.

  The production company also suffers from uncertainty in the cost, volume of production, sales, and availability of raw materials and workers number because they vary according to the seasons of the year.

  I had adopted in this research fuzzy linear program model with fuzzy figures

This paper studies a novel technique based on the use of two effective methods like modified Laplace- variational method (MLVIM) and a new Variational method (MVIM)to solve PDEs with variable coefficients. The current modification for the (MLVIM) is based on coupling of the Variational method (VIM) and Laplace- method (LT). In our proposal there is no need to calculate Lagrange multiplier. We applied Laplace method to the problem .Furthermore, the nonlinear terms for this problem is solved using homotopy method (HPM). Some examples are taken to compare results between two methods and to verify the reliability of our present methods.

Algorithms using the second order of B -splines [B (x)] and the third order of B -splines [B,3(x)] are derived to solve 1' , 2nd and 3rd linear Fredholm integro-differential equations (F1DEs). These new procedures have all the useful properties of B -spline function and can be used comparatively greater computational ease and efficiency.The results of these algorithms are compared with the cubic spline function.Two numerical examples are given for conciliated the results of this method.

The aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.

     Meerkat Clan Algorithm (MCA) is a nature-based metaheuristic algorithm which imitates the intelligent behavior of the meerkat animal. This paper presents an improvement on the MCA based on a chaotic map and crossover strategy (MCA-CC). These two strategies increase the diversification and intensification of the proposed algorithm and boost the searching ability to find more quality solutions. The 0-1 knapsack problem was solved by the basic MCA and the improved version of this algorithm (MCA-CC). The performance of these algorithms was tested on low and high dimensional problems. The experimental results demonstrate that the proposed algorithm had overcome the basic algorithm in terms of solution quality, speed a

       In this paper, we apply a new technique combined by a Sumudu transform and iterative method called the Sumudu iterative method for resolving non-linear partial differential equations to compute analytic solutions. The aim of this paper is to construct the efficacious frequent relation to resolve these problems. The suggested technique is tested on four problems. So the results of this study are debated to show how useful this method is in terms of being a powerful, accurate and fast tool with a little effort compared to other iterative methods.