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

Main Article Content

S. O. Ajibola
A. S. Oke
W. N. Mutuku

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

Article Details

How to Cite
Ajibola, S. O., Oke, A. S., & Mutuku, W. N. (2020). LHAM Approach to Fractional Order Rosenau-Hyman and Burgers’ Equations. Asian Research Journal of Mathematics, 16(6), 1-14. https://doi.org/10.9734/arjom/2020/v16i630192
Section
Original Research Article

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