Radiation amplification law for inverted media of fractal structure, obtained using $d$-analysis

Optical properties of homogeneous fractals are investigated. The law of radiation amplification in inverted media, which are homogeneous fractals, has been generalized. So this law is specified as the law of Bouguer-Lambert-Bееr for fractal environments. The law has resulted from local fractional analysis based on $d$-operator. The $d$-operator is generalized by differentiation and integration in view of any permanent complex orders. For $d$-operator correspondence principle is performed that provides derivatives and integrals of classical analysis if the order is $1$.