E. Karimov :Multivariate Mittag-Leffler type functions associated with Prabhakar Fractional Calculus

Date: Friday, 30 May, 2025 - 15:00 to 16:00 CEST
Title : Multivariate Mittag-Leffler type functions associated with the Prabhakar Fractional Calculus
Speaker: Erkinjon Karimov, Ghent University

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy
Organizers : Pavan Pranjivan Mehta* and Arran Fernandez**
SISSA, International School of Advanced Studies, Italy
** Eastern Mediterranean University, Northern Cyprus

Keywords: Multivariate Mittag-Leffler type functions, Prabhakar Fractional Calculus, Fractional-order differential equations

Abstract

Certain bivariate and trivariate Mittag-Leffler-type functions are investigated, focusing on their Euler-type integral representations [1], [2], as well as upper and lower estimates [3]. These functions arise in the solutions of differential equations involving the Prabhakar fractional derivative [4]. We demonstrate how the derived estimates can be applied to solve direct and inverse problems for sub-diffusion and fractional wave equations [3], [5], [6], as well as for certain combinations of these equations [7].

Biography

Dr. Erkinjon Karimov is a Researcher specializing in partial differential equations of integer and fractional order and special functions, connected with such PDEs. He is affiliated with Ghent University, where he conducts research on direct and inverse problems for PDEs. Dr. Karimov has published more than 50 papers, contributing to advancements in direct and inverse problems for fractional-order PDEs and mixed-type PDEs.

Dr. Karimov holds a Ph.D. (2006) and D.Sc. (2020) from V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, where he focused on direct and inverse problems for PDEs of various types, including mixed-type. Throughout his career, he has collaborated with researchers from the University of Santiago de Compostela, the University of Las Palmas de Gran Canaria, Sultan Qaboos University, etc. His projects have been supported by the State Agency for Science and Technology of the Republic of Uzbekistan, ICMS (Great Britain), ICTP (Italy), TWAS-CAS (China). In addition to his research, Dr. Karimov is actively involved in teaching, mentoring, and managing scientific journals (https://mib.mathinst.uz), demonstrating his commitment to education and the development of future scientists. More information can be found at https://sites.google.com/view/erkinjo...

Bibliography

[1] A. Hasanov, E. Karimov, Euler-type integral representations for bi-variate Mittag-Leffler-type functions, Cybernetics and Systems Analysis 61(3) (2025), pp. 74–84.
[2] A. Hasanov, E. Karimov, On generalized Mittag-Leffler type functions of two variables, arXiv:2501.03918 (2025).
[3] A. Hasanov, E. Karimov, On a boundary-value problem in a bounded domain for a time-fractional diffusion equation with the Prabhakar fractional derivative, Bulletin of the Karaganda university: Mathematics series, 111(3) (2023), pp. 39–46.
[4] E. Karimov, N. Tokmagambetov, M. Toshpulatov, On a Mixed Equation Involving Prabhakar Fractional Order Integral-Differential Operators, Trends in Mathematics: Extended Abstracts 2021/2022. APDEGS 2021, 2(25) (2023), pp. 221–230.
[5] E. Karimov, K. Turdiev, D. Usmonov, Nonlocal problem for the time-fractional generalized telegraph equation with the Prabhakar fractional derivative, arXiv:2503.08274 (2025).
[6] E. karimov, K. Turdiev, Inverse problem for the time-fractional generalized telegraph equation, ResearchGate: DOI 10.13140/RG.2.2.18122.89285 (2025).
[7] E. Karimov, N. Tokmagambetov, M. Toshpulatov, Mixed partial differential equation: Forward problem linked with the wave-diffusion process, ResearchGate: 387959072 (2025)