@article{Roul2011,
  author    = {Roul, Pradip},
  title     = {Numerical solutions of time fractional degenerate parabolic equations by variational iteration method with Jumarie-modified Riemann-Liouville derivative},
  series = {Mathematical methods in the applied sciences},
  volume    = {34},
  journal   = {Mathematical methods in the applied sciences},
  number    = {9},
  publisher = {Wiley-Blackwell},
  address   = {Malden},
  issn      = {0170-4214},
  doi       = {10.1002/mma.1418},
  pages     = {1025 -- 1035},
  year      = {2011},
  abstract  = {In this article, the fractional variational iteration method is employed for computing the approximate analytical solutions of degenerate parabolic equations with fractional time derivative. The time-fractional derivatives are described by the use of a new approach, the so-called Jumarie modified Riemann-Liouville derivative, instead in the sense of Caputo. The approximate solutions of our model problem are calculated in the form of convergent series with easily computable components. Moreover, the numerical solution is compared with the exact solution and the quantitative estimate of accuracy is obtained. The results of the study reveal that the proposed method with modified fractional Riemann-Liouville derivatives is efficient, accurate, and convenient for solving the fractional partial differential equations in multi-dimensional spaces without using any linearization, perturbation or restrictive assumptions.},
  language  = {en}
}
@article{SandevTomovskiDubbeldametal.2018,
  author    = {Sandev, Trifce and Tomovski, Zivorad and Dubbeldam, Johan L. A. and Chechkin, Aleksei V.},
  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}
}