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.

Sodium Dodecyle Sulphate (CH3(CH2)11SO4-Na+) solution was used as a secondary oil recovery by using a lab Model shown in figure-1. The effect of (solution concentration, temperature and salinity) on interfacial tension figure-2 and figure-3 and figure-4 respectively. The best values of these three variables, were taken (those values that give the lowest interfacial tension). Porosity, saturation, permeability were determined in the lab depending on Darcy law. Primary oil recovery was displaced by water until no more oil is obtained then sodium dodecyle sulphate solution was injected. The total oil recovery was 94.8% or 85.7% of the residual oil (secondary oil recovery) figure-5. This method was applied on Iraqi oil field and it gave resu

    The main purpose of the work is to apply a new method, so-called LTAM, which couples the Tamimi and Ansari iterative method (TAM) with the Laplace transform (LT). This method involves solving a problem of non-fatal disease spread in a society that is assumed to have a fixed size during the epidemic period. We apply the method to give an approximate analytic solution to the nonlinear system of the intended model. Moreover, the absolute error resulting from the numerical solutions and the ten iterations of LTAM approximations of the epidemic model, along with the maximum error remainder, were calculated by using MATHEMATICA® 11.3 program to illustrate the effectiveness of the method.

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 this paper, a method based on modified adomian decomposition method for solving Seventh order integro-differential equations (MADM). The distinctive feature of the method is that it can be used to find the analytic solution without transformation of boundary value problems. To test the efficiency of the method presented two examples are solved by proposed method.

The aim of this paper is to propose a reliable iterative method for resolving many types of Volterra - Fredholm Integro - Differential Equations of the second kind with initial conditions. The series solutions of the problems under consideration are obtained by means of the iterative method. Four various problems are resolved with high accuracy to make evident the enforcement of the iterative method on such type of integro differential equations. Results were compared with the exact solution which exhibits that this technique was compatible with the right solutions, simple, effective and easy for solving such problems. To evaluate the results in an iterative process the MATLAB is used as a math program for the calculations.

     Task scheduling in an important element in a distributed system. It is vital how the jobs are correctly assigned for each computer’s processor to improve performance. The presented approaches attempt to reduce the expense of optimizing the use of the CPU. These techniques mostly lack planning and in need to be comprehensive. To address this fault, a hybrid optimization scheduling technique is proposed for the hybridization of both First-Come First-Served (FCFS), and Shortest Job First (SJF). In addition, we propose to apply Simulated Annealing (SA) algorithm as an optimization technique to find optimal job’s execution sequence considering both job’s entrance time and job’s execution time to balance them to reduce the job

Cantilever beams are used in many crucial applications in machinery and construction. For example, the airplane wing, the microscopic probe for atomic force measurement, the tower crane overhang and twin overhang folding bridge are typical examples of cantilever beams. The current research aims to develop an analytical solution for the free vibration problem of cantilever beams. The dynamic response of AISI 304 beam represented by the natural frequencies was determined under different working surrounding temperatures ((-100 ℃ to 400 ℃)). A Matlab code was developed to achieve the analytical solution results, considering the effect of some beam geometrical dimensions. The developed analytical solution has been verified successful