@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{RoulSchinnerKassner2011,
  author    = {Roul, Pradip and Schinner, Alexander and Kassner, Klaus},
  title     = {Simulation of the strain distribution under a two-dimensional sand pile},
  series = {Powder technology : an international journal on the science and technology of wet and dry particulate systems},
  volume    = {214},
  journal   = {Powder technology : an international journal on the science and technology of wet and dry particulate systems},
  number    = {3},
  publisher = {Elsevier},
  address   = {Lausanne},
  issn      = {0032-5910},
  doi       = {10.1016/j.powtec.2011.08.039},
  pages     = {406 -- 414},
  year      = {2011},
  abstract  = {We study the averaged macroscopic strain tensor for a sand pile consisting of soft convex polygonal particles numerically, using the discrete-element method (DEM). First, we construct two types of "sand piles" by two different pouring protocols. Afterwards, we deform the sand piles, relaxing them under a 10\% reduction of gravity. Four different types of methods, three best-fit strains and a derivative strain, are adopted for determining the strain distribution under a sand pile. The results of four different versions of strains obtained from DEM simulation are compared with each other. Moreover, we compare the vertical normal strain tensor between two types of sand piles qualitatively and show how the construction history of the piles affects their strain distribution.},
  language  = {en}
}