Speaker: Emilia Bazhlekova, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

Time : 16:00 - 17.00 CEST (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

Zoom link : A link will appear here, one hour before the talk

Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords:  multinomial Mittag-Leffler function, multi-term fractional evolution equation, completely monotone function, Bernstein function

Abstract: The multinomial Mittag-Leffler function, introduced by Yu. Luchko and R. Gorenflo [1], plays a crucial role in the study of evolution equations with multiple fractional time-derivatives. In this talk we first discuss basic properties of this function with main focus on representation of solutions to multi-term fractional evolution equations in terms of functions of this type and useful estimates.  Next, the Prabhakar type generalization of the multinomial Mittag-Leffler function is introduced [2,3]. Its complete monotonicity is studied, based on Bernstein functions' technique [2]. Asymptotic estimates are also given. The presented results extend known properties of the classical Mittag-Leffler function. In addition, we give an example from Physical Chemistry, where multinomial Mittag-Leffler type functions naturally emerge, as well as applications in linear viscoelastic models [4].

Biography: Emilia Bazhlekova is a Full Professor, Doctor of Sciences, at the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences. She received PhD degree in 2001 from Eindhoven University of Technology, The Netherlands. Her PhD thesis “Fractional evolution equations in Banach spaces” is cited more than 900 times. The main field of research of E. Bazhlekova is Fractional Calculus and its applications (analysis of (generalized) fractional evolution equations, subordination principle, operational calculus approach, applications of Fractional Calculus in linear viscoelasticity) with research results published in about 50 papers in international peer-reviewed scientific journals with more than 1000 citations. She is an associate editor of the international journal “Fractional Calculus and Applied Analysis”.

Bibliography

[1] Y. Luchko, R. Gorenflo. “An operational method for solving fractional differential equations with the Caputo derivatives”. In: Acta Math. Vietnamica 24 (1999), pp. 207–233.
[2] E. Bazhlekova. “Completely monotone multinomial Mittag-Leffler type functions and diffusion equations with multiple time-derivatives”. In: Fract. Calc. Appl. Anal. 24 (2021), pp. 88–111. https://doi.org/10.1515/fca-2021-00051
[3] E. Bazhlekova, I. Bazhlekov. “Identification of a space-dependent source term in a nonlocal problem for the general time-fractional diffusion equation”, In: J. Comput.Appl. Math. 386 (2021), 113213. https://doi.org/10.1016/j.cam.2020.113213
[4] E. Bazhlekova, S. Pshenichnov. “Wave propagation in viscoelastic half-space with memory functions of Mittag-Leffler type”. In: Int. J. Appl. Math. 34 (2021), pp.423–440. https://doi.org/10.12732/ijam.v34i3.1