Impact of Hajj on Muslims With Special Reference to Pakistan

Hajj is one of the five pillars of Islam and is obligatory, once in life time, on adult Muslims having physical and financial capacity. Historically, ‘Hajj’ has been a rigorous undertaking. Although technological advancement has made it easier in many ways, yet there are hardships owing to ever increasing number of pilgrims visiting Makkah Mukkaramah i.e. A city with finite resources including all available resources. The Government of Pakistan, being a facilitator, endeavors to make the Hajj experience as comfortable as is possible within the resources available and standards affordable by Pakistani Hujjaj by making extensive arrangements, through a transparent process, so that the pilgrims could perform their manasik-e-Hajj as enshrined in Quran and Sunnah. The Pilgrim accounts stress that the Hajj leads to a feeling of unity with fellow Muslims.  It increases belief in equality and harmony among ethnic groups and Islamic sects and leads to more favorable attitudes toward all the people of Pakistan including   women with greater acceptance of female education and employment. Hajjis show increased belief in peace, and in equality and harmony among adherents of different religions. The evidence suggests that these changes are more a result of exposure to and interaction with Hajjis from around the world, rather than religious instruction or a changed social role of pilgrims upon their return to Pakistan.

Study of Arbitrary Order Differential Equations Via Iterative Technique and Optimal Homotopy Asymptotic Method

In this dissertation, the concerned study of the research dealts with various types of the boundary value problems of nonlinear fractional-order differential equations. Almost for all kinds of arbitrary order differential equations, this study emphasize on existence theory, various aspect of Ulam stability, lower and upper solutions, iterative schemes and analytical methods of perturbation. We have developed strong sufficient conditions for the uniqueness and existence of upper and lower solutions for the fractional differential equations, with the help of classical fixed point theorem and monotone iterative method. A strong attention has also been given to the numerical solution of fractional differential equations and frac tional partial differential equations. In this regard, some powerful and an efficient numerical techniques have been established for the approximate solutions of both linear and nonlinear fractional order differential equations. One of them, an established technique is based on monotone sequence and one of them from pertubation method is based on homotopy defini tion and an known deformation equation to obtain the solutions in the form of convergent series. Both the methods are interesting and efficient for solving nonlinear fractional-order differential equations. In pertubation method, we have developed a new method for FPDEs which is known as Optimal Homotopy asysmptotic method OHAM based on homotopy def inition and an known deformation equation. With the help of afore mentioned techniques and methods, we solved both linear and nonlinear ordinary as well as partial fractional order differential equations. We considered some fractional order differential equations for illustrative purposes and numerical approximations of their solutions are tabulated and plotted via MATLAB softwares. The numerical results obtained via aforesaid techniques, are compared with other standard techniques. Which shows, that how these techniques are more effective and reliable, than the standard ordinary differential equations solvers.