Description
A Master of Science in Mathematics by Abrar Ansar entitled, “Classical and Modified Fractional Differential Transform Methods: Applications to Health-related Problems, including covid-19 and Bromsulfthalein (BSP) Studies”, submitted in November 2023. Thesis advisor is Dr. Marwan Abukhaled. Soft copy is available (Thesis, Completion Certificate, Approval Signatures, and AUS Archives Consent Form).
Abstract
The present thesis employs the Fractional Differential Transform Method (FDTM) to address two health-related problems. The FDTM was initially applied to the linear fractional human liver model, resulting in a semi-analytic approximate solution. Secondly, it was successively applied to a non-linear fractional COVID-19 model over a prolonged time span with the goal of observing the convergence of the approximate solution. In both applications, the results obtained by the FDTM demonstrated a high level of precision when compared to the fourth order Runge-Kutta (RK4) method for the integer order α = 1. Furthermore, we analyzed the effects of the FDTM solution on various fractional values of α and found that the hereditary properties of fractional differential equations are preserved. In addition, this thesis discusses some important properties of the solution for both models.