Anomalous diffusion in nonhomogeneous media: Power spectral density of signals generated by time-subordinated nonlinear Langevin equations

• We obtained time-subordinated nonlinear SDEs generating signals with power law distributions.
• The analytical expression of power spectral density has been derived.
• For some parameters our equations generate signals having 1/f1/f spectrum.

Subdiffusive behavior of one-dimensional stochastic systems can be described by time-subordinated Langevin equations. The corresponding probability density satisfies the time-fractional Fokker–Planck equations. In the homogeneous systems the power spectral density of the signals generated by such Langevin equations has power-law dependency on the frequency with the exponent smaller than 1. In this paper we consider nonhomogeneous systems and show that in such systems the power spectral density can have power-law behavior with the exponent equal to or larger than 1 in a wide range of intermediate frequencies.