Fractional differential equations have gained significant attention in recent years due to their ability to model various physical phenomena involving memory and non-locality accurately. Timefractional heat-like and wave-like equations are significant as they describe critical processes in diverse fields such as physics, engineering, and biology. This research article introduces a novel Sumudu transform iterative method for calculating semi-analytic soluton of time-fractional heatlike and wave-like equations. By harnessing the power of the Sumudu transform and iterative techniques, this method offers a promising approach to solving such equations effectively, enabling better understanding and analysis of complex dynamical systems.