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THE DIRIHLET PROBLEM FOR THE FRACTIONAL POISSON’S EQUATION WITH CAPUTO DERIVATIVES: A FINITE DIFFERENCE APPROXIMATION AND A NUMERICAL SOLUTION

ABSTRACT
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.
KEYWORDS
PAPER SUBMITTED: 2011-04-21
PAPER REVISED: 2011-07-14
PAPER ACCEPTED: 2011-07-18
DOI REFERENCE: https://doi.org/10.2298/TSCI110421076B
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2012, VOLUME 16, ISSUE 2, PAGES [385 - 394]
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