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Approximating Solutions of an Initial Value Problem Through Modified Adomian Decomposition Method and Artificial Neural Network Technique

Year: 2026

Type: article

Abstract: This study explores and compares two numerical methods for approximating solutions to fractional integro-differential equations with initial conditions. The first method is a modified version of the Adomian decomposition method (ADM), which improves convergence by refining the decomposition series and efficiently computing Adomian polynomials. The second approach leverages artificial neural networks (ANN), utilizing their universal approximation property to construct solutions based on optimized weight and bias parameters. By applying these methods to various test cases, we evaluate their effectiveness in handling complex nonlinear problems. The numerical results highlight the accuracy and reliability of both techniques, offering insights into their practical applications in solving fractional differential equations.

Source: Fractals

DOI: 10.1142/s0218348x26400207

Authors: ABDALLAH BENSAYAH, BRAHIM TELLAB, JESSADA TARIBOON, MOHAMMAD ESMAEL SAMEI, SINA ETEMAD

Institutions: University of Ouargla, King Mongkut's University of Technology North Bangkok, Bu-Ali Sina University, Cyprus International University, Jadara University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

OpenAlex ID: W7128766166

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