## An approximate solution for a fractional diffusion-wave equation using the decomposition method.(English)Zbl 1071.65135

Summary: The partial differential equation of diffusion is generalized by replacing the first order time derivative by a fractional derivative of order $$\alpha$$, $$0 < \alpha \leqslant 2$$. An approximate solution based on the decomposition method is given for the generalized fractional diffusion (diffusion-wave) equation. The fractional derivative is described in the sense of M. Caputo [Linear models of dissipation whose $$Q$$ is almost frequency independent. II. J. Roy. Austral. Soc. 13, 529–539 (1967)]. A numerical example is given to show the application of the present technique. Results show the transition from a pure diffusion process $$(\alpha = 1)$$ to a pure wave process $$(\alpha = 2)$$.

### MSC:

 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 35K55 Nonlinear parabolic equations 35K05 Heat equation 26A33 Fractional derivatives and integrals 35L05 Wave equation
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### References:

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