مولانا شبلی نعمانی کے چند تفردات اور ضعف استدلال سیرۃ النبی کی روشنی میں ایک ناقدانہ جائزہ

Maulānā Shiblī Nu‘mānī (1914) was a great Muslim scholar of sub-continent. Shiblī was a versatile scholar in Arabic, Persian, Turkish and Urdu. He collected much material on the life of Prophet of Islam, Muhammad (ﷺ) but could write only first two volumes of the planned work the Sirat-un-Nabi(ﷺ). His disciple Syed Sulaymān Nadvī, made use of this material and added to it and also wrote remaining five volumes of the work, the Sīrat Al-Nabī(ﷺ) after the death of his mentor. Shiblī was greatly inspired by the progress of science and education in the West. He wanted to inspire the Muslims to make similar progress by having recourse to their lost heritage and culture, and warned them against getting lost in the Western culture. The writer of this article has written a preface followed by an introduction of life and work of Maulānā Nu‘mānī. The next part consists of explaining distinctive features of Shiblī’s book. Maulānā Nu‘mānī dedicated his entire life for the sake of Islam. He had a high quality awareness of the Quran and Sunnah. In his book “Sīrat Al-Nabī", he proved his uniqueness (tafarrudat) regarding various Islamic teachings. In this article I have endeavored to collect some of his uniqueness (tafarrudat) on various issues. Maulānā Nu‘mānī's uniqueness and exclusive ideas were unacceptable for many of contemporary scholars and traditional religious leadership. This article contains some of the selected religious issues in which Shiblī has differed, on the basis of arguments from Quran and Hadith, from traditional scholars. In this article I have analysed Allama's such ideas from his original writings.

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.