Speaker: Syed Abbas, Indian Institute of Technology Mandi

Time : 15:00 - 16.00 CEST (Rome/Paris)

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

Zoom :  A zoom meeitng 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:  Julia set, fractional derivative, Escape time algorithm

Abstract: The filled Julia set of the complex map f : C→C is defined as the set of initial points such that trajectories starting from this point will be bounded. The boundary of this filled-Julia set is called the Julia set, and the complement of the filled Julia set is called the Fatou set. In this talk, we describe various fractional derivatives and the discrete versions of those fractional derivatives. This presentation describes the fractional map to generate the Julia set by using the escape-time algorithm. The obtained Julia sets are highly sensitive to the parameter values. Using the same approach, we will generate the Julia set of the discrete fractional model. After generating Julia sets, we will control them by designing various controllers. The control of Julia sets is obtained by using the stability of fixed points. Also, the complete synchronization of Julia sets of two different systems is studied in this talk. 

Biography: Currently working as a Professor in the School of Mathematical and Statistical Sciences, IIT Mandi since January 2023. I have worked as Associate Professor from October 2017 to January 2023 and Assistant Professor from August 2010 to October 2017 in the School of Basic Sciences at Indian Institute of Technology Mandi. I received my M.Sc. and PhD in Mathematics from Indian Institute of Technology Kanpur in 2004 and 2009 respectively. I have worked as a postdoctoral fellow at University of Bologna, Italy, visiting scientists at TU Dresden, Germany and research associate at University of Fribourg, Switzerland. My teaching experience includes several graduates and under graduate courses. I received excellence in teaching award for undergraduate teaching. The core areas of my research are delay/functional/abstract differential equations, Ecological modelling, Difference equations, Stochastic control. My research focuses are delay, functional, and abstract differential equations, ecological Modeling, structured population model, time scale calculus and nonlinear analysis.

Bibliography

[1] Kumar, M., Abbas, S. (2025). Fractal dimension and control of Julia set generated by the discrete competitive model. Numerical Algorithms, 1-36. 

[2] Kumar, M., Abbas, S. (2024). Adaptive synchronization and anti-synchronization of Julia sets generated by the competitive model. Physica Scripta, 99(11), 115231. 

[3] Kumar, M. and Abbas, S., 2025. Fractal dimension and control of Julia set of discrete fractional tumor-immune model. Discrete and Continuous Dynamical Systems-S, pp.0-0.