Speaker: Walaa Yasin, Department of Mathematics, Palestine Technical University

Time : 15:00 - 16:00 CEST (Rome/Paris)

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

Zoom : A Zoom 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: fractional calculus, d-bar derivatives, radial derivatives, quaternionic analysis, Clifford analysis

Abstract: The standard definitions of fractional derivatives and integrals are well-suited for real analysis, but they lack direct analogues for fundamental operators in complex and hypercomplex analysis, such as the Cauchy–Riemann system and the d-bar derivative. In this talk, I present a unified framework for fractional d-bar operators across complex, quaternionic, and Clifford settings. We introduce fractional powers of the d-bar and radial derivatives through binomial-type series constructions, which naturally generalize the classical integer-order operators. These definitions are rigorously justified by establishing semigroup properties, composition laws, and their action on special functions, including Fueter polynomials. The talk will demonstrate how these operators bridge fractional calculus with hypercomplex function theory, with brief remarks on ongoing work regarding fractional Cauchy–Kovalevskaya extensions. These developments open new avenues for applications in mathematical physics, boundary value problems, and signal processing.

Biography: Walaa Yasin is a Palestinian mathematician who earned her Ph.D. in Mathematics from Eastern Mediterranean University (2025), with a thesis titled "Fractionalizing Complex Analysis on Clifford Algebras," supervised by Arran Fernandez. She holds an M.Sc. in Mathematics from Birzeit University (2018) and a B.Sc. in Pure Mathematics from An-Najah National University (2015). Her research focuses on fractional calculus and hypercomplex analysis, specializing in the combination of fractional operators with quaternionic, Clifford, and bicomplex function theory. She also has interests in Lie symmetry methods, difference equations, and automata theory. During her doctoral studies, she was awarded a BAP-C scientific research grant (Hypercomplex Analysis, Transforms, and Spaces – HATS) from Eastern Mediterranean University to support international collaborations in her field. In 2024, she received the Grunwald-Letnikov Award for Best Student Paper (theoretical track) at the 12th IFAC Conference on Fractional Differentiation and Its Applications (ICFDA) in Bordeaux, France. Since completing her PhD, she has continued to work on extending fractional calculus to bicomplex and polyanalytic settings, and investigating CK extensions and Fischer decompositions in fractional Clifford analysis.

Bibliography

[1] Fernandez, A., Bouzouina, C.: Fractionalisation of complex d-bar derivatives. Complex Variables and Elliptic Equations 66(3), 437–475 (2021).
[2] Fernandez, A., G¨uder, C., Yasin, W.: Fractional powers of the quaternionic d-bar derivative. Advances in Applied Clifford Algebras 34, 2 (2024).
[3] Yasin, W., & Fernandez, A. (2025). Fractional powers of Clifford d-bar and radial derivatives. Journal of Mathematical Analysis and Applications, 542(2), 128952