In the fascinating world of mathematics, there are individuals who delve into the intricate realms of fluid mechanics and fractional calculus—and I count myself among them. Everyday phenomena, such as pouring honey from a jar or observing the steady flow of a river, conceal rich mathematical structures beneath their surface. Uncovering these hidden principles is what continually reminds me why I am drawn to applied mathematics.My academic journey began with a strong foundation in mathematics and culminated in the completion of my M.Phil. degree in Applied Mathematics from Abdul Wali Khan University of Mardan, where I graduated with a CGPA of 3.67 out of 4.00. During this period, I developed a deep appreciation for mathematical modeling and its power to explain complex physical processes.My M.Phil. research focused on the analysis of couple stress fluid flow in inclined Poiseuille configurations under the influence of magnetohydrodynamics (MHD). In simple terms, this work examined how fluids with microstructural effects behave when flowing through inclined channels in the presence of magnetic fields. Such flows arise in numerous engineering and geophysical applications, where classical fluid models fail to capture the underlying physics. By incorporating couple stress effects and magnetic forces, my research contributed to a more realistic and nuanced understanding of fluid behavior under complex conditions.This research involved the formulation of governing equations, analytical and semi-analytical solution techniques, and computational validation. Through this work, I strengthened my expertise in fluid mechanics, fractional calculus, differential equations, and applied mathematical analysis, while gaining hands-on experience with advanced mathematical modeling.Building upon this foundation, I am currently pursuing a PhD at the University of Adelaide, South Australia, Australia. My doctoral research is centered on analytical modelling of underground carbon dioxide (CO₂) storage in aquifers, a topic of critical importance for climate change mitigation and sustainable energy systems. My PhD work focuses on developing and analyzing mathematical models that describe multiphase flow, transport phenomena, and long-term stability of CO₂ sequestration in porous media, with an emphasis on analytical and semi-analytical approaches.