Analytical Solutions of Fractional Riccati Differential Equations via the Laplace Adomian Decomposition Method

In this paper, we successfully implemented the Laplace Adomain Decomposition Method (LADM) to find the approximate and exact solutions for fractional and integer-order differ-ential equations. The numerical data and graphical plots clearly illustrate that the proposed scheme is highly efficient, robust, and reliable. From the comparative analysis and graphical trends, it can be concluded that the integer-order LADM (α = 1.0) provides exceptional accuracy and an almost perfect match with the exact analytical solution during the initial time steps (t  0.5). While the integer-order solution experiences minor truncation errors as time progresses, the fractional-order models (α = 0.5 and α = 0.75) display unique geometric trajectories that converge closely toward the exact solution near the upper bound of the domain. Ultimately, LADM provides powerful, rapidly converging series solutions that are highly effective for modeling complex fractional-order behaviors in real physical applications.

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