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This research paper introduces and compares the efficacy of two techniques, namely the Laplace Variational Iteration Method (LVIM) and the Laplace Homotopy Permutation Method (LHPM), in obtaining approximate solutions for fractional differential equations (FDEs) incorporating the Atangana-Baleanu fractional derivative in the Caputo sense (ABCO). The Atangana-Baleanu fractional derivative, a specialized form of fractional calculus, offers a more accurate representation of anomalous diffusion processes. The LVIM and LHPM are employed to tackle fractional differential equations, which frequently arise in diverse scientific and engineering disciplines. The LVIM combines the advantages of the Laplace transform and the variational iteration technique to yield a reliable and efficient solution strategy. On the other hand, the LHPM integrates the Laplace transform and the homotopy permutation technique to address the same class of equations.This paper provides a detailed exposition of both methodologies, including their algorithmic frameworks and computational procedures. The comparison of the two techniques involves assessing their performance in approximating solutions to fractional differential equations with the Atangana-Baleanu fractional derivative. The obtained results underscore the success of both methods in yielding accurate and practical approximate solutions for this specific type of fractional differential equation.
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