Pusat Pengajian Sains Matematik - Tesis

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New Generalized Differential Transform Method For Solving Fractional Ordinary Differential Equations
(2025-06)
Abuualshaikh, Ammar Jamil Ahmad
Fractional differential equations (fdes) have garnered significant attention in recent years due to their ability to model nonlocal and memory-dependent phenomena in various scientific and engineering domains. Unlike classical differential equations, fdes involve derivatives of non-integer order, leading to intricate and novel mathematical properties. This unique characteristic has allowed fdes to find successful applications in fields such as control theory, chemistry, economics, physics, finance, medicine, and biology. Consequently, there is a pressing need for innovation and the development of accurate and efficient solution techniques for these types of differential equations. However, one of the main challenges in dealing with fdes is the scarcity of exact solutions, mainly due to the complex nature of the real-world problems they represent. To address these challenges, the main goal of this thesis is to introduce a novel method called the new generalized differential transform method (ngdt). The ngdt method utilizes the riemann-liouville derivative (rld) and is designed to offer analytical or numerically approximated solutions for particular instances of ordinary fdes, whether in linear or nonlinear form.