## Analytical solution for the time-fractional telegraph equation.(English)Zbl 1190.35224

Summary: We discuss and derive the analytical solution for three basic problems of the so-called time-fractional telegraph equation. The Cauchy and Signaling problems are solved by means of superposition of of the Laplace and Fourier transforms in variable $$t$$ and $$x,$$ respectively. The appropriate structures and negative properties for their Green functions are provided. The boundary problem in a bounded space domain is also solved by the spatial Sine transform and temporal Laplace transform, whose solution is given in the form of a series.

### MSC:

 35R11 Fractional partial differential equations 35A22 Transform methods (e.g., integral transforms) applied to PDEs 35C10 Series solutions to PDEs 35A08 Fundamental solutions to PDEs
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### References:

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