Solving fractional differential equations using iterative homotopy analysis method / Lee Meng Oon

• Main Author: Lee , Meng Oon
• Format: Thesis
• Published: 2021
• Subjects: QA Mathematics
• Online Access: http://studentsrepo.um.edu.my/13457/2/Lee_Meng_Oon.pdf; http://studentsrepo.um.edu.my/13457/1/Lee_Meng_Oon.pdf; http://studentsrepo.um.edu.my/13457/

Solving fractional differential equations (FDEs) using homotopy analysis method has been a challenging issue. It is mainly related to the difficulty of evaluation and low convergence rate at necessarily high order approximations. This research proposes iterative homotopy analysis method (IHAM) to fill the gap in the existing approach. At each iteration, an optimal convergence control parameter is computed that corresponds to a global minimum error of solution. When a fractional derivative of a function is much harder to evaluate, especially those involving both left-handed and right-handed fractional derivatives, it is possible to approximate the function through Taylor expansion. Numerical comparisons were conducted through various FDEs selected from the literature. The presented results conclude that IHAM delivers faster convergence and better accuracy. We hope that this study will initiate further research to identify other properties that would lead to a stable analytical method for FDEs.