الاباحة في الشريعة الإسلامية والقانون الوضعي

Permissibility (al-Ibāḥah) is a kind of the Islamic law, which gives option to someone to do or not to do something. If something is done by someone under this order, no punishment or reward is liable. It nullifies the delinquency. This paper defines the lexical and technical meanings of permissibility as defined by different Islamic scholars like alShāṭibī, al-Āmidī and al-Ghazālī and the conventional law that how it removes responsibility of delinquency of an act and makes it permissible for person, who does it. Its different kinds and causes for permissibility have been discussed. It has general and particular kinds. It has also been differentiated from insanity: that when a person commits an offense under defective understanding such as childhood, mental illness and in sleeping. These conditions remove someone’s responsibility and one cannot be prosecuted by both the laws. Different rules regarding mistake and ignorance in the case of al-Ibāḥah (permissibility) has been discussed in detail. There are limitations of al-Ibāḥah and if the limits of alIbāḥah are transgressed, then, the act converts into criminality. The author, in this paper, presents a comparative study of the Islamic Law and Conventional Law on the issue of al-Ibāḥah.

A Study of Nonlinear Partial Differential Equations for Exact Solutions

This study is dedicated to the subject of constructing exact solutions of nonlinear partial differential equations arising in engineering science, mathematical physics, fluid mechanics, quantum mechanics etc. The significance of nonlinear partial differential equations lies in the fact that the mathematical modeling of many real life phenomena involves differential equations. Several new nonlinear evolution equations are reported to appear in recent scientific studies. The investigation of exact solutions of nonlinear partial differential equations is of great value in understanding widely different physical phenomena. In late years, many fractional order evolution equations are applied successfully to model various physical phenomena. The memory effects of the fractional derivatives play an important role in understanding mechanical and electrical attributes of actual materials. The aim of this dissertation is to extract the exact solutions of some important nonlinear partial differential equations of integer order as well as non-integer order, for instance the nonlinear short-pulse equation, nonlinear fractional biological population model, the nonlinear complex Ginzburg-Landau equation, the generalized fractional Zakharov-Kuznetsov equation, time-fractional Chan-Allen equation, the fractional dispersive modified Benjamin-Bona-Mahony equation and (2 + 1)−dimensional solution equation. Some well known integration techniques are implemented in carrying out the travelling wave solutions of these equations. The obtained solutions may be worthwhile for explanation of some physical phenomena accurately.