KEYWORDSFractional heat-like equations; Caputo derivative; Mittag-Le er functions; Homotopy perturbation method; Sumudu transform method.Abstract. In this paper, we propose an algorithm to nd approximate solutions of the proposed system of the fractional heat-like equations. The proposed algorithm, basically, illustrates how the two powerful algorithms, the Homotopy Perturbation Method (HPM) and the Sumudu Transform Method (STM), can be combined and used to get exact solutions of fractional partial di erential equations. We also present some examples to illustrate the accuracy and the e ectiveness of this algorithm.