Solutions of the main boundary value problems for the time-fractional telegraph equation by the green function method

What is it about?

The inhomogeneous time-fractional telegraph equation with Caputo derivatives with constant coefficients is considered. For the considered equation, general representation of regular solution in rectangular domain is obtained and the fundamental solution is presented. Using this representation and the properties of the fundamental solution, the Cauchy problem and the main boundary value problems in half-strip and rectangular domains are studied.

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Why is it important?

Equations of such form are used to describe anomalous diffusion processes observed in experiments related to blood circulation, iterated Brownian motion, and telegraph processes with Brownian time.

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