On the analytical solution of Fornberga€“Whitham equation with the new fractional derivative

摘要

Motivated by the simplicity, natural and efficient nature of the new fractional derivative introduced by R Khalil et al in J. Comput. Appl. Math. 264, 65 (2014), analytical solution of space-time fractional Fornberga€“Whitham equation is obtained in series form using the relatively new method called q-homotopy analysis method (q-HAM). The new fractional derivative makes it possible to introduce fractional order in space to the Fornberga€“Whitham equation and be able to obtain its solution. This work displays the elegant nature of the application of q-HAM to solve strongly nonlinear fractional differential equations. The presence of the auxiliary parameter h helps in an effective way to obtain better approximation comparable to exact solutions. The fraction-factor in this method gives it an edge over other existing analytical methods for nonlinear differential equations. Comparisons are made on the existence of exact solutions to these models. The analysis shows that our analytical solutions converge very rapidly to the exact solutions.