حکم الانتفاع بالمرھون عند الفقهاء: دراسة مقارنة

Islam is a complete code of life and dominant upon all the faculties of life. Along with creed faith and worship, Islam has emphasized on the affairs of daily life. In the connotation of affairs all the components of sale and purchase mentioned in detail. Accordingly, there is a provision if someone sell a thing to another and the buyer is not eligible to pay the price then there should be written a statement in the presence of two witnesses to pay the price in fix time. If there is neither witness nor the arrangement of writing, so there should be mortgaged something from the buyer. When the buyer pay a loan then the seller should return the mortgaged thing. The originality of mortgage is for the protection of loan not for profit. In present era the purpose of mortgage has changed and is done it for getting profit. Although some imams and Ahl-e-Zawaher provide the capacity for getting profit, so the Jamhoor and Ahnaf don’t allow anyone to get it. To change the original shape of mortgage is illegitimate and is considered as usury. If there is no custom in a certain territory and the man who offer loan does not intend to get profit then with the permission of the person who has received loan __provides the facility to get profit, However to avoid this practice is far better in shariah. In the article understudy the originality of mortgage and dissension among different Imams to get profit from it has been discussed. In the end a crucial statement has been mentioned.

Mathematical Modeling of Some Infectious Diseases With Integer and Non-Integer Order Derivatives

Mathematical models play an important role to understand the spread, per sistence and prevention mechanism of infectious diseases. In this thesis, we present some mathematical models and their analysis on the dynamics of Tuberculosis (TB) and Hepatitis B virus (HBV). Firstly, we develop these models with classical integer-order derivative and present a detailed qualita tive analysis including, existence and stability of the equilibria, sensitivity of the model parameters and the existence of the bifurcation phenomena. The threshold quantity also called the basic reproduction numberR0 is presented for each model that shows the disease persistence or elimination for their par ticular cases. Further, we develop some suitable optimal control strategies which would be useful for public health department and other health agen cies, in order to reduce and eradicate TB and HBV from the community. The reported TB infected cases in Khyber Pakhtunkhwa province of Pakistan, for the period 2002-2017 are used to parameterize the proposed TB model and an excellent agreement is shown with the field data. The models are solved numerically using Runge-Kutta order four (RK4) method and numerous nu merical simulations carried out to illustrate the disease dynamics and some of the theoretical results. Mathematical models with fractional differential equations (FDEs) are more realistic and provide comparatively better fit to the real data instead of integer order models. Moreover, FDEs possess the memory effect which plays an essential role in the spreading of a disease. Therefore, the second main mathematical findings of this thesis is that we extend the proposed models using fractional order derivatives considering three different fractional xvi operators namely; Caputo, Caputo-Fabrizio and Atangana-Baleanu-Caputo operators. The proposed fractional models are analyzed rigorously and solved numerically using fractional Adams-Bashforth scheme. The graphical results reveal that the models with fractional derivatives give useful and biologically more feasible consequences.