The significance of cooling system of power plant has vividly diverted the scientists, engineers and researchers because of the experimental analyses and numerical approximations on a cooling system of power plant. In fact, the heat exchange processes inside the condenser take worsening place due to uncontrolled increase of the sulfate ion concentration in cooling water which depends upon two main causes (i) an increase in deposition of calcium salts on the surfaces of heat exchangers/cooling towers (ii) the corrosion of power plants in cooling system. In this manuscript, a fractional modeling of sulfate SO4-2 ions concentration for circulating water in a closed cooling system of a power plant is based on the contributions of modern differentiations of Atangana-Baleanu and Caputo-Fabrizio types. The governing equation of Sulfate SO4-2 ions concentration is converted through the law of conservation of mass for volumetric flow rates using modern fractional differentiations, and then solved analytically by invoking Laplace transform method. An interesting comparative analysis of sulfate SO4-2 ions concentration is explored via Atangana-Baleanu and Caputo-Fabrizio fractional operators. Based on both modern differentiation operators our results suggest few similarities and differences for the removal of Sulfate SO4-2 ions concentration. (C) 2019 Elsevier B.V. All rights reserved.