In the framework of fractional action cosmology, we have reconstructed the scalar potentials and scalar fields, namely, quintessence, phantom, tachyon, k-essence, Dirac-Born-Infeld-essence, hessence, dila- ton field, and Yang-Mills field. To get more physical picture of the variation of the scalar field and potential with time, we express a scale factor in emergent, LOGAMEDIATE, and intermediate scenarios, under which the universe expands differently.