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Application of the Laplace decomposition method for solving linear and nonlinear fractional diffusion-wave equations. (English) Zbl 1231.65179
Summary: The Laplace decomposition method is employed to obtain approximate analytical solutions of the linear and nonlinear fractional diffusion-wave equations. This method is a combined form of the Laplace transform method and the Adomian decomposition method. The proposed scheme finds the solutions without any discretization or restrictive assumptions and is free from round-off errors and therefore, reduces the numerical computations to a great extent. The fractional derivative described here is in the Caputo sense. Some illustrative examples are presented and the results show that the solutions obtained by using this technique have close agreement with series solutions obtained with the help of the Adomian decomposition method.

##### MSC:
 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 35K20 Initial-boundary value problems for second-order parabolic equations 35L20 Initial-boundary value problems for second-order hyperbolic equations 35A22 Transform methods (e.g., integral transforms) applied to PDEs 35R11 Fractional partial differential equations 35K55 Nonlinear parabolic equations
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