Michael Ng - Mathematical Science

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MEIIRKHAN BORIKHANOV

Dr

08/08/1994

17185

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+77477141682

Zh. Kenzhebay 11
Turkestan
Kazakhstan

I am honored to express my interest in participating in the Hong Kong Laureate Forum (HKLF), a distinguished gathering that fosters dialogue between the most brilliant minds of our time and the next generation of scientific leaders.
My research centers on exploring the qualitative properties of solutions to fractional differential equations—particularly those that model anomalous diffusion, memory effects, and spatial heterogeneity in complex physical systems. This area sits at the intersection of applied mathematics and theoretical physics, demanding a nuanced understanding of both classical analytical methods and the emerging framework of fractional calculus.
I was honored to be selected as a participant of the 9th Heidelberg Laureate Forum, where I had the privilege of engaging with Fields Medalists, Abel and Turing Award laureates. That experience significantly influenced my scientific worldview and affirmed my belief in the transformative power of international academic exchange. I see the HKLF as a natural and complementary continuation of that journey—particularly given its focus on the Shaw Prize Laureates, whose foundational contributions to physics, astronomy, and life sciences continue to inspire new directions in scientific thought. Therefore, I see the Hong Kong Laureate Forum as an opportunity to contribute, learn, and grow.

Postgraduate (PhD)

Mathematics

Institute of Mathematics and Mathematical Modeling

Almaty

My current research focuses on the qualitative analysis of solutions to fractional analogues of linear and nonlinear partial differential equations (PDEs). In particular, I am interested in exploring existence, uniqueness, blow-up behavior, asymptotic properties, and regularity of solutions to time-space fractional PDEs, which arise naturally in various complex physical and engineering systems characterized by memory and hereditary effects.

This work involves the study of both local and nonlocal operators, such as Caputo and Riemann–Liouville time-fractional derivatives and fractional Laplacians, in bounded domains and unbounded settings. I aim to develop rigorous mathematical tools for understanding the behavior of solutions under critical and supercritical nonlinearities, as well as investigating the influence of boundary conditions and external forces. My research also extends to semilinear and quasilinear models, including fractional diffusion, wave equations, where standard methods from classical PDE theory need to be extended or modified due to the nonlocal nature of the operators involved.