• Qualitative Analysis of Differential Equations Investigating the theoretical aspects such as existence, uniqueness, and stability of solutions to various types of differential equations. • Numerical Solutions of Classical and Fractional Differential and Integral Equations Developing and implementing computational techniques such as Meshless and Haar wavelets collocation methods to solve both integer- and fractional-order differential and integral equations. • Numerical Simulation of Classical and Fractional Interface Problems Solving elliptic, parabolic, and hyperbolic interface problems in both lower and higher dimensions, with special attention to discontinuities and singularities using Meshless and Haar wavelets collocation methods. • Numerical Modeling and Analysis of Infectious Disease Models Formulating, simulating, and analyzing mathematical models of infectious disease transmission using deterministic and numerical approaches. • Application of Neural Networks (PINNs & ANNs) Utilizing Physics-Informed Neural Networks (PINNs) and Artificial Neural Networks (ANNs) for solving ordinary and partial differential equations, as well as infectious disease models and interface problems