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 frac- tional integro-differential equations with initial conditions. The first method is a modified ver- sion of the Adomian Decomposition Method, which improves convergence by refining the decom- position series and efficiently computing Adomian polynomials. The second approach leverages Artificial Neural Networks, utilizing their universal approximation property to construct solu- tions 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 numer- ical results highlight the accuracy and reliability of both techniques, offering insights into their practical applications in solving fractional differential equations.