بدصورت غربت
یہ کیسی تنہائی ہے
میں یادوں کے سیلاب میں بہتا جا رہا ہوں
میرے ایک ہاتھ میں خواہش اور دوسرے میں محرومیاں ہیں
پائوں میں غربت کی زنجیریں ہیں
گلے میں ضرورتوں کا طوق ہے
مجبوریاںسیاہ حلقے بن کرنکھوں کے گرد لپٹی ہیں
پلکوں پہ جمی اداسی
قطرہ قطرہ پگھلتی کھردرے رخساروں پہ گرتی ہے
میرے نیلے ہونٹ جن پہ دوپہر کی جلتی خشک دڑاڑیں ہیں
The present study highlights to contribution of Qari Muhammad tayyab in Islamic assistance has widened the scope of the study. He was not only a knowledgeable scholar but also a verbose, philosophic, logical and sophisticated speaker. His speeches have disseminated a throng of information among the people. He had a deep concerns with the preaching of Islamic teaching. He remained the part of dewband maddersa for long while, where he replete the student with knowledge of islam in addition, qari Muhammad tayyab was a very innovative and revolutionary poet. His poetic nature can be seen his poetries through his writings۔ Qari has done many comparative studies, such as science and islam, Islam and Christianity, linguistic problems and Hindustan, presidential speech of mumbia and many others studies. His knowledge of history could be Cleary observed in his books of history. Such books include the history of dar-ul–uloom dewband, the history of hijaz muqaddas. His aids in many others fields like Islamic equity, problems of fate, a journey to Afghanistan, the principles of preaching are adorable, tidies. To the gathered and analyzed data, his additions to the Islamic studies are abound and will always enlighten the ways for the scholars and would always appreciate the new researchers.
Nonlinear coupled boundary value problems (BVPs) have very important and interesting aspects in the kingdom of Nonlinear Analysis due to not only the theoretical aspects but also the applications which they have in almost everyeld of science. Problems with coupled boundary conditions (BCs) appear while studying mathematical biology, Sturm-Liouville problems, reaction di usion phenomena, chemical systems, and Lotka-Volterra models. This thesis has two parts. In therst part, the existence results are established for therst{order and the second{order nonlinear coupled BVPs subject to nonlinear coupled BCs. Also in the same part, the existence results are established for the second{order nonlinear coupled BVPs when the nonlinear functions have dependence on therst-order derivative. Multiple approaches are available in the literature to investigate the existence of solutions of nonlinear BVPs, but lower and upper solutions (LUSs) approach is one of the strongest. In this approach the original problem is modi ed logically to a new problem, known as the modi ed problem, then the theory of di erential inequalities with the combination of well-known existence results are applied to establish the existence of solution of the modi ed problem. Finally the solution of the modi ed problem leads to the solution of the original problem. Moreover in therst part of the thesis the treatment of the many di erentrst-order and the second-order nonlinear BVPs are uni ed by developing the idea of coupled LUSs. Under this idea, some monotonicity assumptions are imposed on the arguments of the nonlinear BCs in the presence of the existence of a lower solution and an upper solution to unify the classical existence results for very important types of BVPs, like periodic, anti-periodic, Dirichlet, and Neumann. Several examples are discussed to support the theoretical results. The subject fractional calculus being a generalization of integer-order calculus has numerous applications in almost everyeld of science. Due to the intensive use of fractional order di erential problems (FODPs) in almost everyeld of science including, but not limited to, uid dynamics, physics, aerodynamics, chemistry, mathematical biology, image processing, and psychology, there is a strong motivation for the researchers to develop reliable and e cient numerical methods tond the approximate solutions of FODPs. xii xiii In the second part of the thesis, we consider a generalized class of multi{terms fractional order partial di erential equations (FOPDEs) and their coupled systems. We develop a new numerical method and generalize the corresponding Jacobi operational matrices of integrals and derivatives considered on a rectangular plane. By means of the operational matrices, the considered problem of fractional order is reduced to an algebraic one. Being easily solvable, the associated algebraic system leads tonding the solution of the considered problem of fractional order. Validity of the method is established by comparing our simulation results obtained by using MATLAB softwares with the exact solutions in the literature yielding negligible errors.