امام محمد اور ان کی قرآن فہمی

If any nation has right to be proud of its inheritance of concern and religion so followers of Islam deserve of its glorious inheritance of concern or concentration which is according to international investment enlists the unique and individual employment in the history of human. Its infrastructure, core concern, flexibility, exclusive law ideology, judiciary, common and uncommon solution contains unique supremacy. The base of such amazing and awesome international investment depends on fundamental legislative of Quran. Therefore, such accumulated ideology of all investment, although having opposition and distance owes the struggle and efforts of plenty of religious scholars (Fuqha) who proved surpassing sincerity for the services of knowledge. Imam Muhammad Bin Hassan Shebani the first of these (Fiqah People)eligious scholars who compressed (Islamic Fiqah) Islamic scholars teaching in such an educational way as none of other did it. He left us such a memorable priceless and valuable inheritance which crystal clear proof that he was having the thoughtful legislative mind and had profuse passion of gaining knowledge though he faced massive difficulties even spent his money to acquire knowledge. Besides such prestige and wisdom he was well-versed in Fiqah (deep thinking). His knowledge and services of Fiqah can be manipulated by his figurative and descriptive books which are real assets and fundamental ideology of followers of Imam Abu Abdullah Muhammad bin alhasan alshaibai recently in the explanation ofKitab ullah Imam Muhammad was not uncommon writer that is why he was as much famous but Imam Muhammad was supposed to be best scholar of it.

Spline Solutions for Some Fractional Order Boundary Value Problems

In this thesis, the spline solutions to some fractional order boundary value problems have been proposed using different spline collocation techniques. The Caputo’s definition for fractional order derivatives is used, as it allows imposing the boundary constraint(s) in terms of integer order derivative(s). An efficient technique based on non-polynomial quintic spline functions, comprised of a trigonometric part and polynomial part, has been developed for solving fourth order fractional boundary value problems involving product terms. The C¥ differentiability of the trigonometric part of non-polynomial spline compensates for the loss of smoothness inherent in polynomial spline. The second and fourth order convergence of the presented algorithm has been discussed in detail. Moreover, the approximate solutions of three very important time fractional models, advection-diffusion equation, Allen-Cahn equation and diffusion-wave equation, have been studied by means of redefined and modified forms of cubic B-spline functions. The Caputo time-fractional derivatives have been discretized by finite difference formulations whereas B-spline functions are used for spatial discretization. The unconditional stability and theoretical convergence of proposed numerical algorithms have been proved rigorously. Some test examples have been considered for numerical experiments. The computational results are in line with theoretical expectations and exhibit a superior agreement with the analytical exact solutions as compared to the existing techniques.