## Analytical approximate solution for fractional heat-like and wave-like equations with variable coefficients using the decomposition method.(English)Zbl 1070.65105

Summary: The time fractional heat-like and wave-like equations with variable coefficients are obtained by replacing the first order and second order time derivative by a fractional derivative of order $$\alpha$$, $$0 < \alpha \leqslant 2$$. The applications of the decomposition method are extended to derive analytical solutions in the form of a series with easily computed terms for these generalized fractional equation. Some examples are presented to show the efficiency and simplicity of the method.

### MSC:

 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 35K55 Nonlinear parabolic equations 35L70 Second-order nonlinear hyperbolic equations 26A33 Fractional derivatives and integrals
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### References:

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