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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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