APPROXIMATE ANALYTICAL SOLUTION OF FRACTIONAL GAS DYNAMIC EQUATION BY ELZAKI TRANSFORM HOMOTOPY PERTURBATION METHOD
PRADIP R. BHADANE
Department of Mathematics, K.T.H.M. College, Gangapur Road, Nashik-422002 (MS), India.
KIRTIWANT P. GHADLE *
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad-431004 (MS), India.
*Author to whom correspondence should be addressed.
Abstract
In this paper, a new reliable combination of Homotopy perturbation method and Elzaki transform called Elzaki Transform Homotopy Perturbation Method is presented to solve nonlinear Fractional Gas Dynamic Equation. Here the Caputo sense derivative in fractional gas dynamic equation is handled by Elzaki transform, where as nonlinear part in fractional gas dynamic equation is handled by the Homotopy perturbation method. Use of Homotopy Perturbation Method along with Elzaki transform facilitates the method of solving such types of fractional gas dynamic equations. The new method used and the solution obtained by the new method are presented in the paper. We have compared the steady state solution obtained by the new method with the available solutions obtained by other methods of solving fractional gas dynamic equation. Both the solutions obtained by new method and existing methods are found to be exactly same.
Keywords: Caputo fractional derivative, Elzaki transforms, fractional gas dynamic equation, homotopy perturbation method, Riemann-Liouville fractional integral