(untitled) (Contemporary Mathematics, 2025)
This paper examines the application of algebraic principles to solve nonlinear physical models described by fractional-order differential equations. Utilizing the Aboodh Transform Iteration Method and the Aboodh Residual Power Series Method within the Caputo operator framework, the study explores innovative solutions for these models. By bridging algebraic techniques with advanced mathematical methods, it underscores the power of these approaches in unraveling the complexities of systems governed by fractional calculus. This research not only deepens our understanding of nonlinear phenomena but also opens new avenues for the practical application of algebra in solving real-world challenges, showcasing the boundless potential of mathematical innovation.