In this research, we explore the \( (3+1) \) -dimensional q- \({\textbf{d}}\) eformed \({\textbf{t}}\) anh- \({\textbf{G}} \) ordon equation in its fractional form, employing the Caputo fractional derivative to capture the complex dynamics of the system. The residual power series method ( \(\textsf{RPSM}\) ) is utilized as a semi-analytical technique to construct approximate solutions, demonstrating its efficiency and convergence within the context of fractional nonlinear equations. A comprehensive analysis of the convergence is conducted, establishing a robust theoretical foundation for the investigation. To illustrate the characteristics of the solutions, two-dimensional and three-dimensional graphical representations are provided, highlighting the influence of the fractional and q-deformed parameters. The results underscore the capability of the \(\textsf{RPSM}\) in addressing intricate fractional models and offer meaningful insights into their analytical and numerical properties.
