Approximation Methods For Solving Hiv Infection Models In Fuzzy Environment - Almismaery, Hafed H Saleh (2024)
Fuzzy differential equations (FDEs) have a wide range of applications in physics, applied sciences, and engineering and has become undeniably an essential tool for modelling a wide range of real-life phenomena and even more so, those involved with uncertainties such as HIV infection models. Nevertheless, the majority of mathematical representations for fuzzy HIV infection, as depicted in nonlinear models, suffer from a deficiency in analytical solutions whereby these solutions are frequently elusive. Consequently, the prevalent approach to address fuzzy HIV models involves employing approximation methods, typically through numerical techniques. Such numerical methods yield solutions in numeric values. However, it's important to note that these approximate numerical methods face limitations in directly resolving fuzzy HIV infection models and necessitate the use of discretization or linearization. In contrast, approximate analytical methods prove versatile, as they not only apply to fuzzy HIV models without requiring linearization or discretization but also furnish continuous solutions. Therefore, in this thesis, the approximate analytical methods fuzzy homotopy perturbation method (FHPM), fuzzy variational iteration method (FVIM), and their modified versions are considered for solving several linear and nonlinear fuzzy HIV infection models under the concept of Hukuhara differentiability approach to provide approximate analytical solutions in the form of convergence series solution. The existence and uniqueness of the solution for linear and nonlinear fuzzy HIV infection models in this work have also been investigated.