@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}
}
@article{SandevTomovskiDubbeldametal.2018,
  author    = {Sandev, Trifce and Tomovski, Zivorad and Dubbeldam, Johan L. A. and Chechkin, Aleksei},
  title     = {Generalized diffusion-wave equation with memory kernel},
  series = {Journal of physics : A, Mathematical and theoretical},
  volume    = {52},
  journal   = {Journal of physics : A, Mathematical and theoretical},
  number    = {1},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1751-8113},
  doi       = {10.1088/1751-8121/aaefa3},
  pages     = {22},
  year      = {2018},
  abstract  = {We study generalized diffusion-wave equation in which the second order time derivative is replaced by an integro-differential operator. It yields time fractional and distributed order time fractional diffusion-wave equations as particular cases. We consider different memory kernels of the integro-differential operator, derive corresponding fundamental solutions, specify the conditions of their non-negativity and calculate the mean squared displacement for all cases. In particular, we introduce and study generalized diffusion-wave equations with a regularized Prabhakar derivative of single and distributed orders. The equations considered can be used for modeling the broad spectrum of anomalous diffusion processes and various transitions between different diffusion regimes.},
  language  = {en}
}