انعقاد رمضان و عیدین میں رؤیت قمر كی شرط كی حكمت

According to the Prophetic injunction, the fasting in the month of Ramadan, end of the fasting in that month, and determination of Eid al-Adha date should be based on moon sighting by at least two authentic persons. But due to advanced lunar movement calculations majority of Muslim nations prefer the lunar calendar in determining dates of Ramadan and the two Islamic festivals, 6d al-Filr and Eid al-Adha. This article attempts to prove that a pre-calculated lunar calendar cannot be the basis of determining the dates of the fasting month and Islamic festive days; and the only Islamic way to begin fasting month and celebrate festive days is moonsighting.

Existence Theory and Numerical Solutions of the Fractional Order Mathematical Models

In last few decades, it has been proved that fractional order differential equations and their systems are very important in mathematical modeling various phenomena of biological, chemical and physical sciences. In addition to these, a fractional calculus also contains many applications in various fields of engineering and technology. For this propose , differential equations of fractional order is the point of attention in last few years. This project is related with the study of existence theory and numerical solutions of fractional order differential equations. For this study, we first review some useful definitions, notations and results from fractional calculus. Also for the study of numerical solutions, we use a power full techniques. We start our thesis with the study of existence and uniqueness of positive solutions for simple boundary value problem. Then, we obtain necessary and sufficient conditions for existence of at least three positive solutions for the considered models. To solve coupled systems of nonlinear fractional differential equations, we discussamethodwhichisknownasLaplaceAdomiandecompositionmethod(LADM). LADM is an excellent mathematical tool for solving linear and nonlinear differential equations. This method is a combination of the famous integral transform known as Laplace transform and the Adomain decomposition method. In this method, we handle some class of coupled systems of nonlinear fractional order differential equations. Using the proposed method to obtain successfully an exact or approximate solution in the form of convergence series. Thus, we can easily applyLADMto solveawideclassof nonlinearfractionalorderdifferentialequations.The suggested method is applied without any linearization, discretization and unrealistic assumptions. It has been proved that LADM is vary efficient and suitable to solve non-linear problem of physical nature. Some examples are presented to justify the accuracy and performance of the proposed method.