| Issue |
Math. Model. Nat. Phenom.
Volume 12, Number 3, 2017
Special functions and analysis of PDEs
|
|
|---|---|---|
| Page(s) | 82 - 94 | |
| DOI | https://doi.org/10.1051/mmnp/201712308 | |
| Published online | 31 May 2017 | |
Boundary Value Problem for the Time-Fractional Telegraph Equation with Caputo Derivatives
Institute of Applied Mathematics and Automation of KBSC RAS “Shortanov” Str., 89 A, Nal'chik – 360000, RUSSIA
* Corresponding author. E-mail: mamchuev@rambler.ru
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.
Mathematics Subject Classification: 33R11 / 35A08 / 35A09 / 35C05 / 35C15 / 35E05 / 34A08
Key words: Green function method / Caputo derivative / fractional telegraph equation / general representation of solution / boundary value problems / Green functions
© EDP Sciences, 2017
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