Solving fractional diffusion equation using variational iteration method and adomian decomposition method

Abstract

Fractional calculus has been used in many areas of sciences and technologies. This is the consequences of the elementary calculus. The order of the derivative in elementary calculus is integer, n. The nth derivative was changed to a for fractional calculus, where a is a fraction number or complex number. Fractional diffusion equation is one of the examples of fractional derivative equation. This study will focus on the solving fractional diffusion equation using variational iteration method and Adomian decomposition method to obtain an approximate solution to the fractional differential equation. Graphical output may explain further the results obtained. In certain problems the use of fractional differential equation gives more accurate representation rather than using elementary differential equation. Adomian decomposition method is easier in solving fractional diffusion equation since there is no nonlinear term in the equation. However, variational iteration method is more suitable to be applied in solving fractional derivative equation that consists of nonlinear term.