In this paper, electrochemical impedance responses of subdiffusive phase transition materials are calculated and analyzed for one-dimensional cell with reflecting and absorbing boundary conditions. The description is based on the generalization of the diffusive Warburg impedance within the fractional phase field approach utilizing the time-fractional Cahn–Hilliard equation. The driving force in the model is the chemical potential of ions, that is described in terms of the phase field allowing us to avoid additional calculation of the activity coefficient. The derived impedance spectra are applied to describe the response of supercapacitors with polyaniline/carbon nanotube electrodes.

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The possibility of effective amplification of self similar frequency modulated pulses (FMPs) in longitudinally inhomogeneous active optical waveguides is studied. Peculiarities of the dynamics of parabolic pulses with a constant frequency modulation rate are considered. An optimal profile of variation of the group velocity dispersion was obtained in correspondence with optimal amplification of a similariton like pulse. The use of FMPs in amplifying and longitudinally inhomogeneous optical waveguides with a correspondingly matched profile of normal dispersion of group velocities is shown to be capable of providing for an amplifi cation of subpicosecond pulses up to energies above 1 nJ.

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Pseudo-capacitors with electrodes based on polyaniline and vertically aligned multiwalled carbon nanotubes (PANI/VA-MWCNT) composite are studied. Fractional differential models of supercapacitors are briefly discussed. The appropriate fractional circuit model for PANI/MWCNT pseudo-capacitors is found to be a linearized version of the recently proposed phase-field diffusion model based on the fractional Cahn–Hilliard equation. The temperature dependencies of the model parameters are determined by means of impedance spectroscopy. The fractional-order α is weakly sensitive to temperature, and the fractional dynamic behavior is related to the pore morphology rather than to thermally activated ion-hopping in PANI/MWCNT composite.