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Abstract

This paper compares two semi-analytical methods, the Adomian Decomposition Method (ADM) and the Variational Iteration Method (VIM), for solving linear and nonlinear fractional differential equations. The comparison is based on error reduction, stability, and the effectiveness of each method for different types of equations. Using several examples, along with tables and graphs, the approximate solutions obtained are evaluated and compared with the exact solutions, with all computations performed in Mathematica. The results show that ADM provides an easy, efficient approximation for linear equations without requiring Adomian polynomials. However, for nonlinear equations, VIM converges faster and more accurately by selecting an appropriate Lagrange multiplier. Overall, VIM is identified as the more effective semi-analytical method for solving nonlinear fractional differential equations.

Keywords

Adomian Decomposition Method Linear Fractional Differential Equations Nonlinear Fractional Differential Equations Semi-analytical Methods Variational Iteration Method

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Salehi, M. A., Baidar, A. W., & Noori, N. (2025). A Comparative Study of Variational Iteration and Adomain Decomposition Semi Analytical Methods for Fractional Differential Equations. Journal of Natural Sciences – Kabul University, 8(3), 89–115. https://doi.org/10.62810/jns.v8i3.453
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