@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{TomovskiSandevMetzleretal.2012,
  author    = {Tomovski, Zivorad and Sandev, Trifce and Metzler, Ralf and Dubbeldam, Johan},
  title     = {Generalized space-time fractional diffusion equation with composite fractional time derivative},
  series = {Physica : europhysics journal ; A, Statistical mechanics and its applications},
  volume    = {391},
  journal   = {Physica : europhysics journal ; A, Statistical mechanics and its applications},
  number    = {8},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0378-4371},
  doi       = {10.1016/j.physa.2011.12.035},
  pages     = {2527 -- 2542},
  year      = {2012},
  abstract  = {We investigate the solution of space-time fractional diffusion equations with a generalized Riemann-Liouville time fractional derivative and Riesz-Feller space fractional derivative. The Laplace and Fourier transform methods are applied to solve the proposed fractional diffusion equation. The results are represented by using the Mittag-Leffler functions and the Fox H-function. Special cases of the initial and boundary conditions are considered. Numerical scheme and Grunwald-Letnikov approximation are also used to solve the space-time fractional diffusion equation. The fractional moments of the fundamental solution of the considered space-time fractional diffusion equation are obtained. Many known results are special cases of those obtained in this paper. We investigate also the solution of a space-time fractional diffusion equations with a singular term of the form delta(x). t-beta/Gamma(1-beta) (beta > 0).},
  language  = {en}
}