FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS - A STUDY BY NUMERICAL METHODS

This paper is to prove that, the fractional partial differential equation forms a finite domain with the numerical
solution by using different fractional derivatives. The two fractions are used to prove the fractional diffusion equation and
the fractional dispersion equation. The Fractional Differential Equation is formed from the standard diffusion equation
replacing the order, as a second space derivative, with the fractional derivative
. The analytical solutions of, both the fractional diffusion equa
From these three numerical methods, the L1/L2
method; only the third method is used to deal with the fractional derivative. The two fractional me
system of ordinary differential equations that solves by the graphical method. It concludes by the numerical results, that
have demonstrated the three numerical method’s effectiveness and convergence.
KEYWORDS: Fractional Dispersion Equation, Fractional Derivative, L1/L2
Matrix Transform Method & Graphical Method.