<p>In this study, we explore matter bounce modeling through the lens of fractal gravity. We use a non-zero parameter for the scaling factor. Also describe Type III singular bouncing cosmology evolution. The cosmological bounce occurs in such a way that the bouncing point coincides exactly with Type III singularity point. We derive the related field equations within the framework of the FRW background. Further, we obtained the deceleration parameter, expressions for pressure, density and the Equation of State parameter in terms of cosmic time <i>t</i>. We also analyze the violation of the Null and Strong energy conditions near the bounce, expressing the results in terms of cosmic time <i>t</i>. Additionally, we introduce the state-finder pair to differentiate various dark energy models. Lastly, we investigate the behavior of the adiabatic speed of sound to assess the plausibility of the proposed cosmological bouncing scenario, formulating our analysis in terms of cosmic time <i>t</i>.</p>