Extended Hypergeometric Functions and Orthogonal Polynomials

Dr. Praveen Agarwal earned his Ph. D. in Mathematics at the Malviya National Institute of Technology (MNIT) in Jaipur, India, in 2006. Recently, Prof. Agarwal has been listed as the World's Top 2% Scientist from 2020-2025, released by Stanford University. In the 2025 ranking of best scientists worldwide announced by Research.com, he ranked 13th at the India level and 1297th worldwide in Mathematics. Dr. Agarwal has been actively involved in research as well as pedagogical activities for the last 24 years. His major research interests include Special Functions, Fractional Calculus, Numerical Analysis, Differential and Difference Equations, Inequalities, Probability & Statistics, and Fixed Point Theorems. He has published 11 research monographs and edited volumes and more than 405 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. He has served over 50 Journals in the capacity of an Editor/Honorary Editor, or Associate Editor, and published 15 books as an editor. Clemente Cesarano is an associate professor of numerical analysis at the UNINETTUNO University, where he coordinates the local mathematics section and the doctoral course in technological innovation engineering. He has carried out teaching and research activities in various Italian and European institutions and universities; he has been a visiting professor in some European universities, including the University of Linz and the Complutense University of Madrid. He is the author of over 200 scientific publications texts and manuals in the field of approximation theory and mathematical analysis. He has participated, also as coordinator, in various national and international funded research projects.

• 1. Generalized $k$ type-hypergeometric functions as the Meijer G-function2. Matrix analogue of new class of hypergeometric function3. Some extended type hypergeometric functions of two and three variables4. AN EXTENSION OF k-GAMMA AND k-BETA MATRIX FUNCTION BY USE OF TWO PARAMETER k-MITTAG-LEFFLER FUNCTION5. $k$-TYPE CAPUTO FRACTIONAL DERIVATIVE OPERATOR AND ITS PROPERTIES6. AN EXTENSION OF k-HYPERGEOMETRIC FUNCTIONS7. Certain Pathway Fractional Integral Formulae Involving Extended $k$-Hypergeometric Functions.8. Certain integral transforms for the k- hypergeometric function9. Generalized Riemann- Liouville k- fractional derivative and its properties10. Main Results on U–Bernoulli Korobov-type polynomials and their Approximate Roots11. Solvability of the Cauchy problem for a fractionally loaded equation with variable coefficients12. Inverse problem for the loaded heat conductivity equation with variable coefficients13. Generalized arbitrary order Mittag-Leffler-type function and Marichev-Saigo-Maeda fractional operators14. Fractional Integration and Differentiation of the Generalized Arbitrary Order Mittag-Leffler-Type Function15. Generalized Fractional Order Kinetic Equations Involving Multi-Index Mittag-Leffler Function of Several Variables16. Certain Integrals Involving $k$-type $R$- and $G$-Functions17. Fractional Integrals and Solution of Fractional Kinetic Equations involving R-and G-Functions