@article{PetreskadeCastroSandevetal.2020,
  author    = {Petreska, Irina and de Castro, Antonio S. M. and Sandev, Trifce and Lenzi, Ervin K.},
  title     = {The time-dependent Schr{\"o}dinger equation in non-integer dimensions for constrained quantum motion},
  series = {Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics},
  volume    = {384},
  journal   = {Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics},
  number    = {34},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0375-9601},
  doi       = {10.1016/j.physleta.2020.126866},
  pages     = {9},
  year      = {2020},
  abstract  = {We propose a theoretical model, based on a generalized Schroedinger equation, to study the behavior of a constrained quantum system in non-integer, lower than two-dimensional space. The non-integer dimensional space is formed as a product space X x Y, comprising x-coordinate with a Hausdorff measure of dimension alpha(1) = D -1 (1 < D < 2) and y-coordinate with the Lebesgue measure of dimension of length (alpha(2) = 1). Geometric constraints are set at y = 0. Two different approaches to find the Green's function are employed, both giving the same form in terms of the Fox H-function. For D = 2, the solution for two-dimensional quantum motion on a comb is recovered. (C) 2020 Elsevier B.V. All rights reserved.},
  language  = {en}
}
@article{PetreskaPejovSandevetal.2022,
  author    = {Petreska, Irina and Pejov, Ljupco and Sandev, Trifce and Kocarev, Ljupčo and Metzler, Ralf},
  title     = {Tuning of the dielectric relaxation and complex susceptibility in a system of polar molecules: a generalised model based on rotational diffusion with resetting},
  series = {Fractal and fractional},
  volume    = {6},
  journal   = {Fractal and fractional},
  number    = {2},
  publisher = {MDPI AG, Fractal Fract Editorial Office},
  address   = {Basel},
  issn      = {2504-3110},
  doi       = {10.3390/fractalfract6020088},
  pages     = {23},
  year      = {2022},
  abstract  = {The application of the fractional calculus in the mathematical modelling of relaxation processes in complex heterogeneous media has attracted a considerable amount of interest lately. The reason for this is the successful implementation of fractional stochastic and kinetic equations in the studies of non-Debye relaxation. In this work, we consider the rotational diffusion equation with a generalised memory kernel in the context of dielectric relaxation processes in a medium composed of polar molecules. We give an overview of existing models on non-exponential relaxation and introduce an exponential resetting dynamic in the corresponding process. The autocorrelation function and complex susceptibility are analysed in detail. We show that stochastic resetting leads to a saturation of the autocorrelation function to a constant value, in contrast to the case without resetting, for which it decays to zero. The behaviour of the autocorrelation function, as well as the complex susceptibility in the presence of resetting, confirms that the dielectric relaxation dynamics can be tuned by an appropriate choice of the resetting rate. The presented results are general and flexible, and they will be of interest for the theoretical description of non-trivial relaxation dynamics in heterogeneous systems composed of polar molecules.},
  language  = {en}
}