IJPAM: Volume 98, No. 4 (2015)

ON THE SOLUTIONS OF NON-LINEAR TIME-FRACTIONAL
GAS DYNAMIC EQUATIONS: AN ANALYTICAL APPROACH

Olaniyi Samuel Iyiola
Department of Mathematics and Statistic
King Fahd University of Petroleum and Minerals
Dhahran Dammam, SAUDI ARABIA


Abstract. We consider non-linear homogeneous and non-homogeneous gas dynamic equations of time-fractional type in this paper. The approximate solutions of these equations are calculated in the form of series obtained by q-Homotopy Analysis Method (q-HAM). Exact solution is obtained for time-fractional homogeneous case while for the case of time-fractional non-homogeneous, exact solution is possible for special case. This is due to the ability to control the auxiliary parameter $h$ and the fraction factor present in this method. The presence of fraction-factor in this method gives it an edge over other existing analytical methods for non-linear differential equations. Comparisons are made with several other analytical methods.

Received: September 29, 2014

AMS Subject Classification: 35Q35, 65M99

Key Words and Phrases: gas dynamic equation, fractional derivative, non-homogeneous, q-homotopy analysis method

Download paper from here.




DOI: 10.12732/ijpam.v98i4.8 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 98
Issue: 4
Pages: 491 - 502


Google Scholar; zbMATH; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).