Asian Research Thesis Index

Abstract

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.

Add/Update Thesis