My research lies at the intersection of dynamical systems, time scale calculus, and the analysis of differential equations with applications to real-world phenomena. I have worked extensively and continue to explore the following areas:
- Dynamical Systems and their long-term qualitative behavior.
- Time Scale Calculus, unifying continuous and discrete dynamical frameworks.
- Dynamics of Periodic and Generalized Functions, including almost periodic, pseudo-periodic, and automorphic structures.
- Mathematical Biology Models on Time Scales, focusing on the qualitative dynamics of ecological, epidemiological, and neural systems.
- Stochastic Differential Equations, exploring their fundamental properties and solution behavior.
- Physics-Informed Neural Networks (PINNs) for solving Ordinary Differential Equations (ODEs), Delay Differential Equations, and Partial Differential Equations (PDEs).
- Quantum Physics-Informed Neural Networks (Q-PINNs) for applications in quantum dynamics and complex systems.
I am particularly interested in combining analytical techniques with modern computational tools, including machine learning and neural network-based solvers to better understand complex dynamical behaviors
