August 27, 2026 Thesis Open Access

ASFEW ENDALU KENAHA

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    "description": "<p>ABSTRACT This paper contains the development and application of Adomian Decomposition Method (ADM) to solve fractional-order differential equations (FODEs). Classical differential equations are well-studied, but many natural and engineering processes are better modeled by fractional derivatives, which capture memory and hereditary effects. Because of their capacity to simulate physical phenomena with memory and hereditary characteristics, fractional ordinary differential equations (FODEs), which involve derivatives of non-integers(fractional) order, have attracted a lot of interest. It is a usable system with fractal capacitance, anomalous diffusion, and viscoelastic materials. However, obtaining analytical solutions for fractional differential equations remains a major challenge due to their nonlocal nature and the complexity of fractional operators. To address this problem, this study employs the Adomian Decomposition Method (ADM), a semi analytical iterative technique that decomposes nonlinear terms into rapidly convergent series. The method is applied to fractional differential equations expressed in the Caputo sense, with solutions obtained for both linear and nonlinear cases. The decomposition generates successive terms without requiring linearization or perturbation, thereby simplifying the solution process. The results demonstrate that ADM provides accurate approximations that converge quickly to the exact solution. Moreover, the method captures the influence of different fractional orders (0 &lt; &beta; &le; 1) on the solution behavior, showing how fractional dynamics interpolate between classical integer-order solutions and memory-dependent systems. Simulations were carried out on test problems, and the approximate ADM solutions were compared with exact solutions where available. Tables and plots of errors confirm the reliability and efficiency of the approach. The findings indicate that ADM is a powerful and flexible tool for solving fractional differential equations and can be extended to more complex models in applied mathematics, physics, and engineering. Keyword: Adomian decomposition method, ordinary differential equation, fractional ordinary differential equations, Analytical solutions of FODEs by ADM</p>", 
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    "title": "THE ANALYTICAL SOLUTION OF SOME FRACTIONAL ORDINARY  DIFFERENTIAL   EQUATIONS BY ADOMIAN DECOMPOSITION METHOD", 
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