Applied Mathematics & Information Sciences

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This study developed three semi-analytical algorithms to solve functional integrodifferential equations with variable delays under initial conditions. These algorithms embrace the Laplace Adomian decomposition method (LADM), the modified Laplace Adomian decomposition method (MLADM), and the Laplace variational iteration method (LVIM). Using the suggested approaches, we find the solutions without discretization, transformation, or limiting traditions while considering suitable initial conditions. In addition, the solutions are generated in fast-converging series with easily calculable terms. The proposed methodologies are tested numerically on three numerical applications to prove their efficacy and dependability as well as to compare their computational efficiency. Based on the numerical results, it is evident that the procedures offered are both effective and correct

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