PRAVEEN AGARWAL

Anand International College of Engineering, Jaipur

India

Some Properties and Applications of Extended Hypergeometric Function and Applications

Euler’s beta, gamma functions (hypergeometric functions) are of the important members of the family of special functions and it plays a vital role in the whole theory of special functions.  These hypergeometric functions together with their extension have many applications in research fields such as engineering, chemical, statistics, fractional calculus, and physical problems. In this Symposium, our discuses have been focus on the extended Euler’s beta function, which is developed by using the 2-parameter Mittag-Leffler function as the kernel. We discuss various basic properties and formulas of the extended Euler’s beta function such as integral representations, transformation formulas, and summation formulas. We also introduce the logarithmicconvexity and some important inequalities for this extended Euler’s beta function. Then by using this extended Euler’s beta function as kernel, we have generalized hypergeometric functions and study various properties of these extended hypergeometric functions. For application point of view, we have also derived some relations between this extended Euler’s beta function and extended fractional derivative operators such as Caputo fractional derivative operator and Riemann-Liouville fractional operators.

Keywords: Beta function, Gamma function, fractional calculus

Short bio

Dr. P. Agarwal was born in Jaipur (India) on August 18, 1979. After completing his schooling, he earned his Master’s degree from Rajasthan University in 2000. In 2006, he earned his Ph. D. (Mathematics) at the Malviya National Institute of Technology (MNIT) in Jaipur, India, one of the highest ranking universities in India. Recently, Prof. Agarwal is listed as the World's Top 2% Scientist 2020 and 21, Released by Stanford University

Dr. Agarwal has been actively involved in research as well as pedagogical activities for the last 20 years. His major research interests include Special Functions, Fractional Calculus, Numerical Analysis, Differential and Difference Equations, Inequalities, and Fixed Point Theorems.  He is an excellent scholar, dedicated teacher, and prolific researcher. He has published 9 research monographs and edited volumes and more than 250 publications (with almost 100 mathematicians all over the world) in prestigious national and international mathematics journals. Dr. Agarwal worked previously either as a regular faculty or as a visiting professor and scientist in universities in several countries, including India, Germany, Turkey, South Korea, UK, Russia, Malaysia andThailand.  He has held several positions including Visiting Professor, Visiting Scientist, and Professor at various universities in different parts of the world. Specially, he was awarded most respected International Centre for Mathematical Sciences (ICMS) Group Research Fellowship to work with Prof. Dr. Michael Ruzhansky-Imperial College Londonat ICMS Centre, Scotland, UK, and during 2017-18, he was awarded most respected TUBITAK Visiting Scientist Fellowship to work with Prof. Dr. Onur at AhiEvran University, Turkey. He has been awarded by Most Outstanding Researcher-2018 (Award for contribution to Mathematics) by the Union Minister of Human Resource Development of India, Mr. Prakash Javadekar in 2018. According to Google Scholar, Dr. Agarwal is cited more than 4, 580 times, and on Scopus his work is cited more than 2,689 times.  Dr. Agarwal is the recipient of several notable honors and awards.

Dr. Agarwal provided significant service to Anand International College of Engineering, Jaipur. Under his leadership during 2010-20, Anand-ICEconsistently progressed in education and preparation of students, and in the new direction of academics, research and development. His overall impact to the institute is considerable. Many scholars from different nations,including China, Uzbekistan, Thailand and African Countriescameto work under his guidance.  The majority of these visiting post-doctoral scholars weresent to work under Dr. Agarwal by their employing institutions for at least one month.

Dr. Agarwal regularly disseminates his research at invited talks/colloquiums (over 25 Institutions all over the world).He has been invited to give plenary/keynote lectures at international conferences in the USA, Russia,  India, Turkey, China, Korea, Malaysia, Thailand, Saudi Arabia, Germany, UK, Turkey,  and Japan.

He has served over 50 Journals in the capacity of an Editor/Honorary Editor, or Associate Editor, and published 9 books as an editor. Dr. Agarwal has also organized International Conferences/ workshops’/seminars/summer schools.

In summary of these few inadequate paragraphs, Dr. P. Agarwal is a visionary scientist, educator, and administrator who havecontributed to the world through his long service, dedication, and tireless efforts.