Applied Mathematics & Information Sciences

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In this paper, we consider the time-fractional Harry Dym equation. An analytical solution is obtained in series form using q-Homotopy Analysis Method (q-HAM). The presence of the auxiliary parameter h and the 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. Our error analysis shows that the analytical solution converges very rapidly to the exact solution. Numerical results are obtained using Mathematica 9 and MATLAB R2012b.

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