An Alternating Directions Implicit method is presented to solve the homogeneous heat diffusion equation when the governing equation is a bi-harmonic equation (X) based on Alternative Direction Implicit (ADI). Numerical results are compared with other results obtained by other numerical (explicit and implicit) methods. We apply these methods it two examples (X): the first one, we apply explicit when the temperature .

In this paper, we present an approximate method for solving integro-differential equations of multi-fractional order by using the variational iteration method.
First, we derive the variational iteration formula related to the considered problem, then prove its convergence to the exact solution. Also we give some illustrative examples of linear and nonlinear equations.

in this paper the collocation method will be solve ordinary differential equations of retarted arguments also some examples are presented in order to illustrate this approach

In this paper the modified trapezoidal rule is presented for solving Volterra linear Integral Equations (V.I.E) of the second kind and we noticed that this procedure is effective in solving the equations. Two examples are given with their comparison tables to answer the validity of the procedure.

    In this paper, the finite difference method is used to solve fractional hyperbolic partial differential equations, by modifying the associated explicit and implicit difference methods used to solve fractional  partial differential equation. A comparison with the exact solution is presented and the results are given in tabulated form in order to give a good comparison with the exact solution

          In the present research, a crane frame has been investigated by using finite element method. The damage is simulated by reducing the stiffness of assumed elements with ratios (10% and 20 %) in mid- span of the vertical column in crane frame. The cracked beam with a one-edge and non-propagating crack has been used. Six cases of damage are modeled for crane frame and by introducing cracked elements at different locations with ratio of depth of crack to the height of the beam (a/h) 0.1, 0.20. A FEM program coded in Matlab 6.5 was used to model the numerical simulation of the damage scenarios. The results showed a decreasing in the five natural frequencies from undamaged beam which means

Decision making is vital and important activity in field operations research ,engineering ,administration science and economic science with any industrial or service company or organization because the core of management process as well as improve him performance . The research includes decision making process when the objective function is fraction function and solve models fraction programming by using some fraction programming methods and using goal programming method aid programming ( win QSB )and the results explain the effect use the goal programming method in decision making process when the objective function is
fraction .

       Two new halogenated azo-Schiff ligands were prepared in two steps. The first step included a condensation between 4-amino acetophenone and 2-fluoro-4-bromo aniline to give the corresponding Schiff base. In the second step, the diazonium salt of this Schiff base reacted with 2-naphthol and 4,5-diphenylimidazole to form two new azo-Schiff base derivatives as ligands; (3-((E)-(4-((E)-1-((4-bromo-2-fluorophenyl) imino)ethyl) phenyl) diazenyl) naphthalen-2-ol (HSBAN) (L1) and ((E)-N-(4-bromo-2-fluorophenyl)-1-(4-((E)-(4,5-diphenyl-1H-imidazol-2-yl)diazenyl) phenyl) ethan-1-imine) (HSBAI) (L2), respectively. These new ligands were characterized by mass spectrometry, FT-IR, 1H NMR, UV-Visible spectroscopy and elemental microanalysi