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The time fractional wave-like differential equation with a variable coefficient is studied analytically. By using a simple transformation, the governing equation is reduced to two fractional ordinary differential equations. Then the homotopy analysis method is employed to derive the solutions of these equations. The accurate series solutions are obtained. Especially, when ℏf=ℏg=−1, these solutions...
Here an analytic technique, namely the homotopy analysis method (HAM), is employed to solve the non-linear Thomas–Fermi equation. A new kind of transformation is being used here which has improved the results in comparison with Liao's work. We also present the comparison of this work with some well-known results and prove the importance of this transformation and the freedom of HAM.
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