The linear non-polynomial spline is used here to solve the fractional partial differential equation (FPDE). The fractional derivatives are described in the Caputo sense. The tensor products are given for extending the one-dimensional linear non-polynomial spline to a two-dimensional spline  to solve the heat equation. In this paper, the convergence theorem of the method used to the exact solution is proved and the numerical examples show the validity of the method. All computations are implemented by Mathcad15.

    This paper deals with finding an approximate solution to the index-2 time-varying linear differential algebraic control system based on the theory of variational formulation. The solution of index-2 time-varying differential algebraic equations (DAEs) is the critical point of the equivalent variational formulation. In addition, the variational problem is transformed from the indirect into direct method by using a generalized Ritz bases approach. The approximate solution is found by solving an explicit linear algebraic equation, which makes the proposed technique reliable and efficient for many physical problems. From the numerical results, it can be implied that very good efficiency, accuracy, and simplicity of the pre

This research presents a new study in reactive distillation by using consecutive reaction: the saponification reaction of diethyl adipate (DA) with sodium hydroxide solution .

The effect of three parameters were studied through a design of experiments applying 2³ factorial design . These parameters were : the mole ratio of DA to NaOH solution (0.1 and 1) , NaOH solution concentration (3 N and 8 N) , and batch time (1.5 hr. and 3.5 hr.) . The conversion of DA to sodium monoethyladipate(SMA)(intermediate product) was the effect of these parameters which was detected . Also , the percentage purity of the intermediate product was recorded . The results showed that increasing mole ratio of DA to NaOHsolutio

In a world of fierce competition companies of different activities strive to strengthen their competitiveness in order to be able to deliver greater value to their customers and gain a distinct sites in competition with other companies in the market at the local and international levels. Every company seeks to focus on one or more of the competitive capabilities in order to turn it into an obvious advantage or a number of competitive advantages to contribute in improving the performance and superiority over its competitors. Therefore, the management of companies no longer need only useful information for the internal aspects of the environment, but also need to include the external environment that includes various and constantly changin

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Praise be to God, Lord of the Worlds, and prayers and peace be upon the Master of Messengers, and upon his family and companions

And whoever follows his guidance until the Day of Judgment. As for what follows: Islamic law commands Muslims to unite, reject disagreement, and not dispute, and to spread the spirit of tolerance and love among them. God Almighty said: “And hold fast to the rope of God all of you and do not become divided, and remember the favor of God upon you when you are enemies and He has joined your hearts.” So, by His grace, you became brothers (1), and He said: (And You will be like those who became divided and disagreed after the clear proofs had come to them. It is they - for them is a great punishment.) (2