Michal Fečkan has been a Professor of Mathematics at the Department of Mathematical Analysis and Numerical Mathematics in the Faculty of Mathematics, Physics and Informatics at the Comenius University in Bratislava, Slovak Republic since 2003. He received the master’s degree from Comenius University in Bratislava in 1985 and PhD from the Mathematical Institute of Slovak Academy of Sciences in Bratislava, Slovak Republic in 1993. He is interested in nonlinear functional analysis, bifurcation theory, dynamical systems, and fractional calculus with applications to mechanics, vibrations, and economics. He is the Highly Cited Researcher in Mathematics. His major contributions are as follows
• Existence and bifurcations of periodic, subharmonic, and chaotic solutions for a broad variety of nonlinear problems, including non-smooth mechanical systems with dry frictions; weakly coupled oscillators; systems with relay hysteresis; differential equations on infinite lattices; blue sky catastrophes for reversible dynamical systems; buckling of beams; and discontinuous wave equations, systems with impacts and impulses, implicit differential equations.
• Existence and asymptotic behaviour of solutions of fractional difference, fractional integral, fractional differential, fractional evolution equations and inclusions.
• Extension of classical Hermite-Hadamard type inequalities to the fractional case.
• Iterative learning control and its applications to the new equations such as fractional order equations and inclusions, impulsive equations, delay equations, and multi-agent systems.
• Travelling wave solutions for differential equations on lattices modelled by metamaterials, discrete nonlinear Schrödinger equations, Fermi-Pasta-Ulam models, and fractional differential equations on lattices, with both local and nonlocal couplings.
• Numerical study of discrete, continuous, and fractional order evolutional equations depending on parameters: bifurcations, chaos, hidden attractors.
Some of these results are presented in his books:
M. Fečkan: Topological Degree Approach to Bifurcation Problems, Berlin, Springer, 2008.
M. Fečkan: Bifurcation and Chaos in Discontinuous and Continuous Systems, Berlin, HEP-Springer, 2011.
M. Fečkan, M. Pospíšil: Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems, Amsterdam, Academic Press, 2016.
M. Fečkan, J.R. Wang, M. Pospíšil: Fractional-Order Equations and Inclusions, Berlin/Boston, Walter de Gruyter GmbH, 2017.
P. Olejnik, J. Awrejcewicz, M. Fečkan: Modeling, Analysis and Control of Dynamical Systems: With Friction and Impacts, New Jersey: World Scientific Series on Nonlinear Science Series A: Vol 92, World Scientific Publishing Co. Pte. Ltd., 2018.
J.R. Wang, M. Fečkan: Fractional Hermite-Hadamard Inequalities, Berlin/Boston, Walter de Gruyter GmbH, 2018.
J.R. Wang, M. Fečkan: Non-Instantaneous Impulsive Differential Equations, Basic theory and computation, IOP Publishing Ltd, Bristol, 2018.
J.R. Wang, S. Liu, M. Fečkan: Iterative Learning Control for Equations with Fractional Derivatives and Impulses, Springer Nature, Singapore Pte Ltd., 2022.
The full list of his publications can be found at http://alis.uniba.sk:9909/search/query?locale=en&theme=EPC