Modular stabilities of a reciprocal second power functional equation

In the present work, we propose a different reciprocal second power Functional Equation (FE) which involves the arguments of functions in rational form and determine its stabilities in the setting of modular spaces with and without using Fatou property. We also prove the stabilities in beta-homogenous spaces. As an application, we associate this equation with the electrostatic forces of attraction between unit charges in various cases using Coloumb's law.