A Hybrid Laplace–Adomian Strategy for Nonlinear Fractional Volterra–Fredholm Equations

This paper introduces an enhanced semianalytic method for solving nonlinear fractional Volterra–Fredholm integro-differential equations (NFVFIDEs) by combining the Laplace transform with the regular Adomian decomposition method (ADM) and its accelerated variant (AADM). The key innovation lies in the integration of the Laplace transform with the accelerated Adomian scheme, which generates more iterative terms per computational step, significantly reducing absolute errors compared to classical approaches. Using Caputo fractional derivatives, the approach transforms complex equations into algebraic forms, yielding convergent series solutions. To further improve precision and range, Padé approximations are applied. Validation through benchmark problems confirms that the AADM significantly outperforms the classical ADM in convergence speed and accuracy, even with fewer iterations, providing a robust framework for modeling memory-dependent systems in physics and engineering. Comparative analysis against DTM, PINNs, and other semianalytic methods demonstrates the superior convergence speed and accuracy of the proposed approach.