غزواتِ نبویہ ﷺ میں اہلِ کتاب کے ساتھ اخلاقِ حسنہ کے مظاہر Manifestations of Akhlaq-e-Hasanah (good manners) with the People of the Book (Ehl-e-Kitab) in Ghazwat-e-Nabawiyyah ﷺ

When we study about the life of Holy Prophet (ﷺ), his life demand from Muslims to protect the dignity and honour of their Muslim brothers. They not only protect or care the right of their Muslim brothers in their life but also protect their dignity after their death. In the light of Holy Prophet Life the circle of human rights is so vast. In this, his life teaches us the turidicul, rights, marriage, settlement different between good or evil, isonomy and the verses of martyr and the noble behaviour with Jews and Christians. There is a big role of ethics on the human personality. The ethics is the tester of good or bad person Human with the noble ethics the Muslims. To be remembered as staying up all the night and to fast. The ethics play important role in the life of Human. In the life of Prophet (ﷺ) we know about his good deeds and noble behavior with non Muslims. The success of the Holy Prophet preaching is only because of his ethics and truthness. Islam Universal Religion. It’s Teachings and pregnative system is the everlasting. In this modern period there is no way except Islam to get Rid the unsolved problems of the age. The beloved Prophet (ﷺ) “Sira Mubarak” the way of light only. There is aspect of the life without the real pregnative system. Peace and the War both are in the teaching of the Holy Prophet (ﷺ). Peace, progress contentment, satisfaction, true, unity, brotherhood in the lightment of the “Uswa Hasna”. Let’s seek the real way in our beloved Prophet (ﷺ). Key Words: Holy Prophet, Ghazwa, Akhlaq-e-Hasanah, Ehl-e-Kitab, War, Ethics.

Modeling and Numerical Simulations of Some Fractional Nonlinear Viscoelastic Flow Problems

Modeling of viscoelastic flows in terms of fractional calculus is an inquisitive area in engineering and industry. The physical models with fractional operators in nonNewtonian fluid mechanics represent more realistic behavior of flows involving nonlinear complex dynamics. The efficiency is because of freedom to choose derivative of any order in the mathematical formulation of the flows. Non-integer derivatives are important for the systems having hereditary behavior as they depend on the past conditions along with the local conditions. Viscoelastic fluids keep memory of old deformations and their behavior is related to these deformations. The fractional derivatives are more adequate in predicting the characteristics of viscoelastic fluids than the ordinary derivatives. In literature linear flow problems, with non-integer derivatives are solved by classical transforms methods. Unfortunately, most of the viscoelastic fluids unlike Newtonian fluids, are not characterized by only one relation. Mathematical equations, for the viscoelastic fluid flows are highly nonlinear in nature. In most of situations, highly nonlinear PDEs cannot be solved exactly, by existing techniques. Literature survey indicates, that appropriate consideration is not given to the numerical solutions, of anomalous nonlinear flow problems with noninteger derivatives. In this study, we have modeled the viscoelastic flow problems via fractional calculus approach and considered numerical techniques using finite difference approximations along with ”L1 algorithm”to discretize non-integer derivatives of time and finite element, discretization is used for space variables, in order to solve the governing fractional viscoelastic models. Finally we have predicted the behavior of viscoelastic fluids that can be used directly for the simulations of industrial processes.