On the analytical solution of Fornberg–Whitham equation with the new fractional derivative

Pramana

Olaniyi Samuel Iyiola1¹  Gbenga Olayinka Ojo¹ 

[1]Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, KFUPM, Dhahran, Saudi Arabia$$

关键词: Fornberg–Whitham equation;    fractional derivative;    q-homotopy analysis method;    h-curve.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 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 Fornberg–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 Fornberg–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.

【 授权许可】

Unknown