APPROXIMATING SOLUTIONS OF AN INITIAL VALUE PROBLEM THROUGH MODIFIED ADOMIAN DECOMPOSITION METHOD AND ARTIFICIAL NEURAL NETWORK TECHNIQUE

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.