A kind of irregular scaling equations with physical feasibility is introduced and studied to describe the rational iterative process of fractional-order operators. Several new Frantance Approximation Circuits(FACs) are put forward and described by generalized irregular scaling equations. A class of irregular scaling equations based on the unknown parameters mn is extended, and the characteristics of the rational iterative processes of the fractional order operators described by this type of equation are studied. Four new FACs are obtained by replacing the position of the components of the known FACs, and described by the corresponding generalized irregular scaling equations. Research shows that generalized irregular scaling equations have different approach solutions. Finally, the optimization methods for the algebraic iterative processes of impedance functions described by generalized irregular scaling equations are introduced. Based on the new FACs, several design schemes of arbitrary-order scaling fractal FACs with high operational constancy are proposed. A simulation experiment of fractional-order differential circuit is designed to verify the operational performance of the new FACs.