TY - JOUR
TI - The Dirihlet problem for the fractional Poisson’s equation with Caputo derivatives: A finite difference approximation and a numerical solution
AU - Beibalaev V D
AU - Meilanov R P
JN - Thermal Science
PY - 2012
VL - 16
IS - 2
SP - 385
EP - 394
PT - Article
AB - A finite difference approximation for the Caputo fractional derivative of the 4-β, 1 < β ≤ 2 order has been developed. A difference schemes for solving the Dirihlet’s problem of the Poisson’s equation with fractional derivatives has been applied and solved. Both the stability of difference problem in its right-side part and the convergence have been proved. A numerical example was developed by applying both the Liebman and the Monte-Carlo methods.