Laplace homotopy perturbation method for Burgers equation with space- and time-fractional order
Johnston S. J.,
Jafari H.,
Moshokoa S. P.,
Ariyan V. M.,
Baleanu D.
Affiliations
Johnston S. J.
Department of Mathematical Sciences, University of South Africa, PO Box 392, UNISA 0003, Africa
Jafari H.
Department of Mathematical Sciences, University of South Africa, PO Box 392, UNISA 0003, Africa
Moshokoa S. P.
Department of Mathematics and Statistics, Faculty of Science, Tshwane University of Technology, Arcadia Campus, Building 2-117, Nelson Mandela Drive, Pretoria 0001, Africa
Ariyan V. M.
Department of Mathematical Sciences, Mangosuthu University of Technology, Umlazi, Africa
Baleanu D.
Department of Mathematics and Computer Science Çankaya University, Ankara, Turkey
The fractional Burgers equation describes the physical processes of unidirectional propagation of weakly nonlinear acoustic waves through a gas-filled pipe. The Laplace homotopy perturbation method is discussed to obtain the approximate analytical solution of space-fractional and time-fractional Burgers equations. The method used combines the Laplace transform and the homotopy perturbation method. Numerical results show that the approach is easy to implement and accurate when applied to partial differential equations of fractional orders.
