استنباط احکام میں حضرت عائشہ کا منہج قرآن کریم کی روشنی میں

In this article an effort has been made to describe Hazrat ‘฀ishah (R. A) ’s methodology of derivation of Ahk฀m from Holy Quran. Holy Quran and Sunnah of Holy Prophet (S. A. W) is basic source of Islamic Shar฀‘ah. Hazrat ‘฀ishah Sidd฀qah (R. A) was the wife of the Holy Prophet (S. A. W), and the daughter of Hazrat Ab฀ Bakr (R. A). She spent her time in learning and acquiring knowledge of the two most important sources of Islam, the Qur'an and the Sunnah of His Prophet (S. A. W). Hazrat ‘฀ishah (R. A) narrated 2210 Ah฀d฀th out of which 174 Ah฀d฀th are commonly agreed upon by Bukh฀ri and Muslim. She was an ardent and zealous student of Islamic jurisprudence. She has not only described Ah฀d฀th and reported her observations of events, but interpreted them for derivation of Ahk฀m. Umm Al-Mu’min฀n Hazrat ‘฀ishah (R. A) is a great scholar and interpreter of Islam, providing guidance to even the greatest of the Companions (R. A) of the Holy Prophet Muhammad (S. A. W). She has not only described Ah฀d฀th and reported her observations of events, but interpreted them for derivation of Ahk฀m. Whenever necessary, she corrected the views of the greatest of the Companions of the Holy Prophet (S. A. W). It is thus recognized, from the earliest times in Islam, that about one-fourth of Islamic Shar฀‘ah is based on reports and interpretations that have come from Hazrat ‘฀ishah (R. A). As a teacher she had a clear and persuasive manner of speech. Hazrat ‘฀ishah (R. A) is a role model for women. She taught Islam many people. She was an authority on many matters of Islamic Law, especially those concerning women.

Efficacious Algorithms for the Solutions of Fractional Differential Equations

Fractional calculus is the generalization of integer-order calculus to non-integer order. In recent decades, fractional calculus has re-attracted the attention of scientists and engineers. Due to the nonlocal property, fractional operators give a perfect aid to characterize the memory and hereditary properties of various processes and materials. As a result, and motivated by the increasingly important role played by fractional calculus, mathematicians are constantly developing algorithms for solving fractional differential equations. The objective of this work is to develop the efficacious algorithms for the solutions of both ordinary and partial fractional differential equations. For solving both linear and non-linear fractional differential equations, spline method and residual power series method are used. Matlab, Maple and Mathematica programmes are developed to compute the numerical solutions. The simplicity, efficiency and accuracy of the presented methods are demonstrated by aid of several examples and comparisons are made between exact and numerical solutions.