LHAM Approach to Fractional Order Rosenau-Hyman and Burgers' Equations

Abstract

Fractional calculus has been found to be a great asset in nding fractional dimension in chaos theory, in viscoelasticity di usion, in random optimal search etc. Various techniques have been proposed to solve di erential equations of fractional order. In this paper, the Laplace-Homotopy Analysis Method (LHAM) is applied to obtain approximate analytic solutions of the nonlinear Rosenau-Hyman Korteweg-de Vries (KdV), K(2, 2), and Burgers' equations of fractional order with initial conditions. The solutions of these equations are calculated in the form of convergent series. The solutions obtained converge to the exact solution when α = 1, showing the reliability of LHAM.