منھج الشیخ السھارنفوری فی رفع الشبھات العقلیۃ: دراسۃ تحلیلیۃ فی ضوء ’’بذل المجھود‘‘ نموذج

Explanation of Hadith literature is a very significant academic contribution of Muhadditheen since the dawn of this sacred source. Sunan by Abu Dawod (d. 275 A.H.) has its well reputation in field Hadith codification and it has taken a perpetual attraction of Hadith scholars for its interpretation. Molana Saharanpuri (d.1927A.D.)is a famous sub continental Muslim scholar who contributed a voluminous interpretation titled ‘Bazl al-Majhood’ in which he comprehensively explores different aspect of Hadith. He has given an exploration of intellecttu-al solutions to various doubts and objection in very lucid way. The article has been rendered to focus on the same issue and intends to deal with the method-ology adopted by Saharanpuri while resolving the insinuations regarding Hadith literature.

Fractional Calculus of Extended Mittag-Leffler Functions

In this thesis, we have presented some fractional integral and differential operators with extension of Mittag-Leffler function. The chapter wise summary of this thesis is as under. This thesis consists of seven chapters. The first chapter gives brief introduction about thesis. We have presented a comprehensive Literature review relating to Special functions in brief. In the second chapter, we explore the composition of fractional differential operator known as Caputo-type MarichevSaigo-Maeda operator with extended Mittag-Leffler function. In chapter three, fractional integration known as P d − transform with the extended Mittag-Leffler function is presented. Some corollaries and consequences with already existed extensions of a function are also discussed. In chapter four, composition of fractional integral and differential operator known as Marichev-Saigo-Maeda operators, containing Appell’s function F3 in its kernel with extension of Mittag-Leffler functionare presented. Chapter five and six explain the composition of Weyl fractional operator and Pathway integral operator with the extended Mittag-Leffler function. Chapter seven shows the application of Marichev-Saigo-Maeda differential operator involving incomplete hypergeometric functions. Chapter 2, 3, 4 and 7 are the original parts of the thesis. It should be noted that the results obtained in these Chapters were published in [53], [54], [55] and [52] respectively.