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Analysis of a time fractional wave-like equation with the homotopy analysis method. (English) Zbl 1217.35111

Summary: 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 \(\hbar_{f}=\hbar_{g}=-1\), these solutions are exactly the same as those results given by the Adomian decomposition method. The present work shows the validity and great potential of the homotopy analysis method for solving nonlinear fractional differential equations. The basic idea described in this letter is expected to be further employed to solve other similar nonlinear problems in fractional calculus.

MSC:

35L05 Wave equation
35R11 Fractional partial differential equations
26A33 Fractional derivatives and integrals
34A08 Fractional ordinary differential equations
55P99 Homotopy theory
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