Efficient Computing of Nonlinear Higher-Order Fractional Integro-Differential Equations via Aboodh-ADM Technique

Abstract

This paper introduces a novel semi-analytical method for solving nonlinear higher-order fractional Volterra-Fredholm integro-differential equations (FIDEs) of Hammerstein type. By combining the Aboodh transform with the Adomian Decomposition Method (ADM), the proposed approach efficiently handles Caputo fractional derivatives and nonlocal integral operators. The solution is derived as a rapidly convergent infinite series via the inverse Aboodh transform, offering analytical insight even in the absence of closed-form solutions. Rigorous stability analysis and convergence criteria are established, demonstrating the method’s numerical stability and confirming an algebraic order of convergence dependent on fractional order and discretization parameters. Truncated series solutions yield high-accuracy approximations, validated through numerical examples that highlight the method’s reliability, computational efficiency, and robustness for memory-dependent dynamics. The framework is broadly applicable to engineering and applied mathematics problems requiring precise modeling of nonlocal phenomena.OPEN ACCESS Received: 02/05/2025 Accepted: 25/06/2025 Published: 15/08/2025

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