Dr. Samaira Naz

Basic Information

Brief Statement of research work

My research is broadly situated within the fields of applied mathematics and mathematical analysis, with a particular focus on fractional calculus, integral inequalities, differential equations, and mathematical modeling. A central theme of my work has been the theoretical development and application of generalized fractional operators, especially extensions of the Hilfer-Katugampola derivative framework, through which I have studied Cauchy problems, boundary value problems, and a range of analytic inequalities including Gruss-type, Ostrowski-type, Minkowski-type, and discrete fractional inequalities. These contributions aim to extend classical mathematical results into more flexible and parameter-rich settings that better capture complex real-world phenomena. Alongside this theoretical work, I have engaged actively with computational and applied problems, contributing to the mathematical modeling of hybrid nanofluids and magnetohydrodynamic flows using techniques such as the Galerkin finite element method and spectral collocation, in collaboration with interdisciplinary research teams. More recently, my research interests have expanded into mathematical epidemiology, where I apply fractional differential equation frameworks to model infectious disease transmission and evaluate public health interventions, as well as into biomedical data analysis, including the development of machine learning-based frameworks for medical image classification and integrative statistical methods for clinical diagnosis. Across all these areas, my aim is to advance rigorous mathematical theory while maintaining a strong connection to meaningful real-world applications in science, engineering, and public health.