IJPAM: Volume 98, No. 4 (2015)
GAS DYNAMIC EQUATIONS: AN ANALYTICAL APPROACH
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 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
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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
Pages: 491 - 502