## THERMAL SCIENCE

International Scientific Journal

### 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

**THERMAL SCIENCE** YEAR

**2012**, VOLUME

**16**, ISSUE

**Issue 2**, PAGES [385 - 394]

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