Open AccessLHAM Approach to Fractional Order Rosenau-Hyman and Burgers' Equations
Author(s) -
S. O. Ajibola,
Abayomi Samuel Oke,
Winifred N. Mutuku
Publication year - 2020
Publication title -
asian research journal of mathematics
Language(s) - English
Resource type - Journals
ISSN - 2456-477X
DOI - 10.9734/arjom/2020/v16i630192
Subject(s) - mathematics , fractional calculus , laplace transform , order (exchange) , nonlinear system , homotopy analysis method , burgers' equation , mathematical analysis , partial differential equation , homotopy , pure mathematics , physics , finance , quantum mechanics , economics
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.