<p>Integral transform methods, recognized as a powerful tool in the field of mathematics, are seen as playing a significant role in providing exact solutions to integral equations through the utilization of the unique properties of transforms. In the present research, the Anuj transform has been chosen to address Abel’s integral equation (AIE) within the realm of classical mechanics. This transform is not only easy to apply but also reduces computational cost and computational time. It also provides analytical solutions that are convenient compared to numerical solutions. By delving deep into the intricacies of this transform, the investigation is not only aimed at enhancing the understanding of analytical tools but also at making a distinctive impact on the advancement of computational techniques. This research endeavor is anticipated to contribute significantly to the evolution of analytical methods and to open up new avenues for exploring the intersection of mathematics and classical mechanics.</p>