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Fractional Calculus of Extended Mittag-Leffler Functions

Thesis Info

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Author

Nadir, Aneela

Program

PhD

Institute

National College of Business Administration and Economics

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2019

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/12424/1/Aneela%20Nadir%20Maths%202019%20Ncbae%20lhr%20prr.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726237668

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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.
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