TY  - JOUR
A1  - Roul, Pradip
T1  - Numerical solutions of time fractional degenerate parabolic equations by variational iteration method with Jumarie-modified Riemann-Liouville derivative
JF  - Mathematical methods in the applied sciences
N2  - 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.
KW  - variational iteration method
KW  - biological population equations
KW  - fractional calculus
KW  - exact solution
KW  - Mittag-Leffler function
Y1  - 2011
U6  - https://doi.org/10.1002/mma.1418
SN  - 0170-4214
VL  - 34
IS  - 9
SP  - 1025
EP  - 1035
PB  - Wiley-Blackwell
CY  - Malden
ER  - 
TY  - JOUR
A1  - Roul, Pradip
A1  - Schinner, Alexander
A1  - Kassner, Klaus
T1  - Simulation of the strain distribution under a two-dimensional sand pile
JF  - Powder technology : an international journal on the science and technology of wet and dry particulate systems
N2  - 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.
KW  - Numerical simulation
KW  - Sand pile
KW  - Stress
KW  - Strain
KW  - Granular matter
KW  - Discrete-element method
Y1  - 2011
U6  - https://doi.org/10.1016/j.powtec.2011.08.039
SN  - 0032-5910
VL  - 214
IS  - 3
SP  - 406
EP  - 414
PB  - Elsevier
CY  - Lausanne
ER  -