Abstract
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. For the Cauchy problem theorems of existence and uniqueness of solution are proved, and the explicit form of the solution is constructed. The solutions of the investigated problems are constructed in terms of the appropriate Green functions, which are also constructed in explicit form.
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Mamchuev, M.O. Solutions of the Main Boundary Value Problems for the Time-Fractional Telegraph Equation by the Green Function Method. FCAA 20, 190–211 (2017). https://doi.org/10.1515/fca-2017-0010
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DOI: https://doi.org/10.1515/fca-2017-0010