In this paper, a new technique is offered for solving three types of linear integral equations of the 2^nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree  and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those

This article will introduce a new iteration method called the zenali iteration method for the approximation of fixed points. We show that our iteration process is faster than the current leading iterations  like Mann, Ishikawa, oor, D- iterations, and *-  iteration for new contraction mappings called  quasi contraction mappings. And we  proved that all these iterations (Mann, Ishikawa, oor, D- iterations and *-  iteration) equivalent to approximate fixed points of  quasi contraction. We support our analytic proof by a numerical example, data dependence result for contraction mappings type  by employing zenali iteration also discussed.

In this study, a brand-new double transform known as the double INEM transform is introduced. Combined with the definition and essential features of the proposed double transform, new findings on partial derivatives, Heaviside function, are also presented. Additionally, we solve several symmetric applications to show how effective the provided transform is at resolving partial differential equation.

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

In this paper, our aim is to study variational formulation and solutions of 2-dimensional integrodifferential equations of fractional order. We will give a summery of representation to the variational formulation of linear nonhomogenous 2-dimensional Volterra integro-differential equations of the second kind with fractional order. An example will be discussed and solved by using the MathCAD software package when it is needed.

The university course timetable problem (UCTP) is typically a combinatorial optimization problem. Manually achieving a useful timetable requires many days of effort, and the results are still unsatisfactory. unsatisfactory. Various states of art methods (heuristic, meta-heuristic) are used to satisfactorily solve UCTP. However, these approaches typically represent the instance-specific solutions. The hyper-heuristic framework adequately addresses this complex problem. This research proposed Particle Swarm Optimizer-based Hyper Heuristic (HH PSO) to solve UCTP efficiently. PSO is used as a higher-level method that selects low-level heuristics (LLH) sequence which further generates an optimal solution. The proposed a

This paper aims to propose a hybrid approach of two powerful methods, namely the differential transform and finite difference methods, to obtain the solution of the coupled Whitham-Broer-Kaup-Like equations which arises in shallow-water wave theory. The capability of the method to such problems is verified by taking different parameters and initial conditions. The numerical simulations are depicted in 2D and 3D graphs. It is shown that the used approach returns accurate solutions for this type of problems in comparison with the analytic ones.

The method of solving volterra integral equation by using numerical solution is a simple operation but to require many memory space to compute and save the operation. The importance of this equation appeares new direction to solve the equation by using new methods to avoid obstacles. One of these methods employ neural network for obtaining the solution.

This paper presents a proposed method by using cascade-forward neural network to simulate volterra integral equations solutions. This method depends on training cascade-forward neural network by inputs which represent the mean of volterra integral equations solutions, the target of cascade-forward neural network is to get the desired output of this network. Cascade-forward neural

Summary
The subject ( meaning of added verbs) is one of the main subjects
which study in morphology since in Arabic language. It is include the meaning
of each format, and the increased meaning occurred by this increment in the
verbs.
The (strain) is one of very important meaning in this subject, it takes a
wide area of morphology studies, and interesting of scientists and
researchists.
There are two famous formats for this meaning; (infa la انفع
ل ), and (ifta
la افتع
ل ). Also There are another formats for the same meaning, but less than
the first two in use, they are; (taf ala تفعّ
ل ), (tafa ala تفاع
ل ), (taf lala ) ,(تفعل
ل
ifanlala افعنلل ), (ifanla .(