Time-fractional telegraph equation

What is it about?

In this paper the Green formula for the operator of fractional differentiation in Caputo sense is proved. By using this formula the integral representation of all regular in a rectangular domains solutions is obtained in the form of the Green formula for operator generating the time-fractional telegraph equation. The unique solutions of the initial-boundary value problem with boundary conditions of first kind is constructed. The proposed approach can be used to study the more general evolution FPDE as well as ODE with Caputo derivatives. Boundary Value Problem for the Time-Fractional Telegraph Equation with Caputo Derivatives. Available from: https://www.researchgate.net/publication/309207208_Boundary_Value_Problem_for_the_Time-Fractional_Telegraph_Equation_with_Caputo_Derivatives [accessed Jun 6, 2017].

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Why is it important?

Fractional partial differential equations nd their application in various fields of science, such as physics, chemistry, biology, economy, sociology, etc. Equations of such type are used to describe anomalous diffsion processes observed in experiments related to blood circulation, iterated Brownian motion, and telegraph processes with Brownian time, model of diffusion-drift charge carrier transport in layers with a fractal structure. Note that the fractional advection-dispersion equation with constant coefficients, can be reduced to investigated equation, by changing of unknown function.

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