期刊
AIN SHAMS ENGINEERING JOURNAL
卷 5, 期 3, 页码 999-1004出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.asej.2014.03.014
关键词
Non-homogeneous equation; Gardner equation; Buck-master equation; Fractional derivative; q-Homotopy Analysis Method
资金
- King Fahd University of Petroleum and Minerals (KFUPM)
In this paper, we obtain analytical solutions of homogeneous time-fractional Gardner equation and non-homogeneous time-fractional models (including Buck-master equation) using q-Homotopy Analysis Method (q-HAM). Our work displays the elegant nature of the application of q-HAM not only to solve homogeneous non-linear fractional differential equations but also to solve the non-homogeneous 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 non-linear differential equations. Comparisons are made upon the existence of exact solutions to these models. The analysis shows that our analytical solutions converge very rapidly to the exact solutions. (C) 2014 Production and hosting by Elsevier B.V. on behalf of Ain Shams University.
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