<p>This research presents a novel framework for operational matrices, effectively representing the Atangana-Baleanu fractional derivative within the framework of Genocchi polynomials. These sophisticated operational matrices are utilised to examine the fractional-order Klein-Gordon equation, governed by the Atangana-Baleanu fractional derivative and augmented by an external source term. First, the results for the approximate error are established to assess the adaptability of the method. Further, utilising the collocation technique in conjunction with these operational matrices, the fractional Klein-Gordon equation is reduced to a system of solvable algebraic equations. This system is solved by the software Mathematica using Newton’s method. This research presents comprehensive visualisations of the numerical solutions across multiple scenarios and substantiates the methodology through rigorous error analysis. The accuracy of the proposed method is affirmed by comparing approximate solutions with the exact solutions.</p>