LHAM Approach to Fractional Order Rosenau-Hyman and Burgers' Equations
S. O. Ajibola *
Department of Mathematics, University of Benin, Nigeria.
A. S. Oke
Department of Mathematical Sciences, Adekunle Ajasin University, Nigeria.
W. N. Mutuku
Department of Mathematics and Actuarial Science, Kenyatta University, Kenya.
*Author to whom correspondence should be addressed.
Abstract
Fractional calculus has been found to be a great asset in finding fractional dimension in chaos theory, in viscoelasticity diffusion, in random optimal search etc. Various techniques have been proposed to solve differential 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.
Keywords: Laplace transform, Homotopy Analysis method, Laplace Homotopy Analysis method, Fractional derivative, KdV equation, Burger equation