Speaker: Yuri Luchko, Berlin University of Applied Sciences and Technology, Germany

Time : 14:30 - 15.30 CEST (Rome/Paris)

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

Zoom : A link will appear here, an 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: Sonin condition, general fractional integrals, general fractional derivatives, sequential general fractional derivatives, fundamental theorems of Fractional Calculus, convolution series, convolution Taylor formula, convolution Taylor series.

Abstract: In this talk, we start with a discussion of origins of the general fractional integrals and derivatives with the Sonin kernels in the works by Abel and Sonin. Then some recent results regarding properties of the general Fractional Calculus operators with the Sonin kernels are presented. In particular, the first and the second fundamental theorems of Fractional Calculus for the general fractional derivatives, the regularized general fractional derivatives, and the sequential general fractional derivatives are formulated. As an application, we discuss the convolution series that are a far-reaching generalization of the power law series as well as a representation of functions in form of the convolution Taylor series. Another application is the generalized convolution Taylor formula that contains a convolution polynomial and a remainder in terms of the general fractional integrals and the general fractional sequential derivatives. Finally, we provide a survey of some other recent results devoted to the general Fractional Calculus operators with the Sonin kernels and their applications. 

Biography: Dr. Yuri Luchko is a Full Professor at the Faculty of Mathematics - Physics - Chemistry of the Berlin University of Applied Sciences and Technology in Germany. He studied Mathematics at the Belarussian State University in Minsk and received his PhD degree from the same University in 1993. In 1994, Yuri Luchko got a postdoc position at the Free University of Berlin, Germany, under supervision of Prof. Rudolf Gorenflo and stayed there for six years. From 2000 to 2006, he was a scientific researcher at the University in Frankfurt (Oder), Germany. In 2006, Dr. Yuri Luchko got a professorship at the Technical University of Applied Sciences Berlin, Germany. The main field of his research is Applied Mathematics with a special focus on Fractional Calculus and its applications. Yuri Luchko published about two hundred papers in international peer-reviewed scientific journals and about twenty books and books chapters as author or editor. He is an associate editor of the international journal “Fractional Calculus and Applied Analysis” and editor of several other reputable mathematical journals including ZAA (Zeitschrift für Analysis und ihre Anwendungen).

Bibliography

[1] Y. Luchko. General Fractional Integrals and Derivatives with the Sonine Kernels Mathematics 2021, vol. 9(6), 594.

[2] Y. Luchko. General Fractional Integrals and Derivatives of Arbitrary Order Symmetry 2021, vol. 13(5), 755.

[3] Y. Luchko. Convolution series and the generalized convolution Taylor formula Fract. Calc. Appl. Anal. 2022, vol. 25, 207-228.

[4] Y. Luchko. The 1st level general fractional derivatives and some of their properties J Math Sci 2022, vol. 266, 709-722.