×

A note on “Analytical solution for the time-fractional telegraph equation by the method of separating variables”. (English) Zbl 1486.35425

Summary: J. Chen et al. [ibid. 338, No. 2, 1364–1377 (2008; Zbl 1138.35373)] investigated the analytical solution of the time-fractional telegraph equation with three kinds of nonhomogeneous boundary conditions by the method of separating variables. However, for the Sturm-Liouville eigenvalue problem derived under the Robin boundary conditions, the eigenvalues and eigenfunctions provided by the authors have some defects. In this note, we mainly analyze and modify the eigenvalues and eigenfunctions in detail and obtain the new analytical solution. Numerical experiments show that our new analytical solution is valid.

MSC:

35R11 Fractional partial differential equations
34B24 Sturm-Liouville theory
35L20 Initial-boundary value problems for second-order hyperbolic equations

Citations:

Zbl 1138.35373
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Chen, J.; Liu, F.; Anh, V., Analytical solution for the time-fractional telegraph equation by the method of separating variables, J. Math. Anal. Appl., 338, 2, 1364-1377 (2008) · Zbl 1138.35373
[2] Gu, Q., Mathematical Methods for Physics, 190-208 (2012), Science Press: Science Press Beijing
[3] Podlubny, I., Fractional Differential Equations (1999), Academic Press: Academic Press New York · Zbl 0924.34008
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.