Certain saigo type fractional integral inequalities and their q-analogues

Shilpi Jain; Rahul  Goyal; Praveen Agarwal; Shaher  Momani

doi:10.11121/ijocta.2023.1258

Authors

Shilpi Jain Department of Mathematics, Poornima College of Engineering, Jaipur 302022, India. https://orcid.org/0000-0002-0906-2801
Rahul Goyal Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India. https://orcid.org/0000-0003-0953-751X
Praveen Agarwal Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India. https://orcid.org/0000-0001-7556-8942
Shaher Momani Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordan https://orcid.org/0000-0002-6326-8456

DOI:

https://doi.org/10.11121/ijocta.2023.1258

Keywords:

Saigo fractional integral operator, Riemann-Liouville fractional integral, Erdelyi-Kober fractional integral

Abstract

The main purpose of the present article is to introduce certain new Saigo fractional integral inequalities and their q-extensions. We also studied some special cases of these inequalities involving Riemann-Liouville and Erdelyi-Kober fractional integral operators.

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Author Biographies

Shilpi Jain, Department of Mathematics, Poornima College of Engineering, Jaipur 302022, India.

Shilpi Jain is currently an Associate Professor, Department of Mathematics, Poornima College of Engineering, Jaipur, India. She completed PhD at the University of Rajasthan, Jaipur in 2006. She has more than 18 years of academic and research experience. Her research field is Special Functions and Fractional Calculus. She published more than 70 research papers in the national and international journal of repute.

Rahul Goyal, Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India.

Rahul Goyal is working as Junior Research Fellow (JRF) on the project title “To study the hypergeometric functions and Basic Hypergeometric functions with real and complex analysis (02011/12/2020NBHM (R.P)/R\&D II/7867)” under the supervision of Prof.(Dr.) Praveen Agarwal at Anand International College of Engineering, Jaipur. He received a BSc degree in Physical Science from Ramjas College, University of Delhi, India, and holds an MSc degree in Mathematics from Deshbandhu College, University of Delhi, India. His primary area of interest is special functions and fractional calculus. He has published more than 5 research papers in various international journals and conferences.

Praveen Agarwal, Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India.

Praveen 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 in 2020, 2021 and 2022, 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 has published 11 research monographs and edited volumes and more than 350 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 and Thailand. 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, and Japan. He has served over 50 journals in the capacity of an Editor/Honorary Editor, or Associate Editor, and published 11 books as an editor. He has also organized international conferences/ workshops/seminars/summer schools.

Shaher Momani, Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordan

Shaher Momani received his BSc degree in Mathematics from Yarmouk University in 1984, and his PhD degree in Mathematics from the University of Wales Aberystwyth in 1991. Dr. Momani has published more than 300 articles in ISI international journals of high quality. He has been selected by Clarivate Analytics in its prestigious list of Highly Cited Researchers in Mathematics in 2014, 2015, 2016, and 2017. And in 2018, he has been selected by Clarivate Analytics in the Cross-Field category to identify researchers with substantial influence across several fields during the last decade. Also, he has been selected by Clarivate Analytics in its prestigious list of The World's Most Influential Scientific Minds from 2014 to 2018.

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