فرزند مولانا حبیب الرحمن خان شروانی
ماہ گزشتہ میں ہماری مجلس کے دو محترم ارکان بلکہ اساطین کو ’’وداعِ عزیز‘‘ کے دو جانگزا صدمے برداشت کرنے پڑے، مولانا حبیب الرحمن خان شروانی کو اپنے ’’محبوب‘‘ فرزند کی مفارقت دائمی کا داغ اٹھانا پڑا اور حسام الملک نواب سید علی حسن خان کو اپنے برادر بزگوار نظام الملک نواب سید نورالحسن خان کی دائمی جدائی کا غم سہنا پڑا، یہ دونوں بزرگوار ہماری مجلس کے دست و بازو ہیں، ان کا صدمات سے دو چار ہونا ہمارے لئے لازمۂ غم اور داعیۂ ماتم ہے،
لایحزن اﷲ ’’الحبیب‘‘ فانّنی
لآخذ من حالاتہ بنصیب
مرنے والوں کے لئے دعائے مغفرت انسان کے غم کا علاج نہیں، لیکن اس کی روحانی تشفی کا باعث ہے، اللھم الحقھما بالرفیق الاعلے۔ (سید سليمان ندوی’، نومبر ۱۹۱۷ء)
Pakht┴n society has its own justice system which has different types of penalties and remedies to maintain the justice in the society. This study concentrates to investigate the nature of pecuniary punishment’s practice in distressing issues like killing, civil injuries and criminal offences. Perpetrators are punished to resolve the disputes. On one hand, this paper aims to find out answer to the methods of inflicting decisions in Pakht┴n’s cult and on other hand, to shed light on the legal status of arbitration regarding resolving such issues in the light of Qur’an and Sunnah. Study results illustrate that in some cases the offenders are charged in term of money to facilitate the victims, while in other cases both of the parties, perpetrators and victims, are called upon on meal for reconciliation of their dispute. Besides this, sometimes it is observed that the offenders are not only awarded pecuniary punishment but they are exiled as well.
In this dissertation, we investigate different types of boundary value problems of nonlinear fractional order differential equations. The concerned research is associated to the existence and uniqueness of solutions, Hyers–Ulam type stability and numerical analysis for fractional order differential equations. We develop sufficient conditions for existence and uniqueness of solutions for fractional differential equations, with the help of classical fixed point theory of Laray Schauder type, Banach contraction type and Topological degree method. Further, we investigate the conditions for stability analysis of fractional differential equations. One of the important area of fraction differential equation is known as hybrid fractional differential equation. Hybrid fractional differential equations has an efficient techniques used for modeling various dynamical phenomenon. Therefore, for investigation sufficient conditions for existence and uniqueness of solutions hybrid fractional differential equations, we have used Hybrid fixed point theory established by Dhage and develop sufficient conditions for the existence and uniqueness of solutions of hybrid fractional differential equations. On the other hand, in most cases the nonlinear fractional differential equations are very complicated to obtained an exact analytic solution. Although, if an exact solution is possible, that needed very complicated calculations. Therefore, we paid a strong attention to the numerical solution of fractional differential equations and fractional partial differential equations. We have developed some powerful and an efficient numerical techniques for the approximate solutions of both linear and nonlinear fractional order differential equations. The established technique are based on Laplace transform coupled with Adomain polynomials to obtain the aforesaid solutions in the form of convergent series. Further, we also develop another interesting and useful method based on operational matrices obtained via using Lagendre polynomials. With the help of these mentioned techniques, we solve both linear and nonlinear ordinary as well as partial fractional order differential equations. We consider some fractional order differential equations for illustrative purposes and numerical approximations of their solutions are obtained using MAPLE and MATLAB. The numerical results obtained via aforesaid techniques, are compared with other standard techniques. Which shows, that how the Laplace transform coupled with Adomain polynomials and operational matrices obtained by Legendre polynomials are more effective and reliable, than the standard ordinary differential equations solvers.