Abstract
In this paper, we study the semi-boundless mixed problem for time-fractional telegraph equation. We are able to use the integral transform method (the Fourier sin and cos transforms) to obtain the solution.
Similar content being viewed by others
References
Glockle, W.G., Nonnenmacher, T.F. Fox function representation of non-Debye relaxation processes. J. Stat. Phys, 71(3):741–757 (1993)
Kilbas, A.A., Srivastava, H.M., Trujillo, J.J. Theory and applications of fractional differential equations. Elsevier, Amsterdam, 2006
Kochubei, A.N.K. A Cauchy problem for evolution equations of fractional order. Differential Equations, 25:967–974 (1989)
Mathai. A.M., Saxena.R.K. The H-function with applications in statistics and other disciplines. New Delhi Weley Eastern Limited, 1978
Mainardi. F., Fractional relaxation-oscillation and fractional diffusion-wave phenomena. Chaos, Solitons and Fractals, 7:1461–1477 (1996)
Mainardi, F., Luchko, Yu., Pagnini. G. The fundamental solution of the space-time fractional diffusion equation. Fractional Calculus and Applied Analysis, 4:153–192 (2001)
Moustafa, O.L. On the Cauchy problem for some fractional order partial differential equations. Chaos, Solitons and Fractals, 18:135–140 (2003)
Orsingher, E., Zhao, X., The space-fractional telegraph equation and the related fractional telegraph process. Chinese Ann. Math., (24)B(1):1–12 (2003)
Orsingher, E., Reghin, L. Time-fractional telegraph equations and telegraph processes with brownian time. Probab.Theory Relat.Fields, 128:141–160 (2004)
Pshu, A.V., Solutions of a boundary value problem for a fractional partial differential equation. Differential Equations, 39(8):1150–1158 (2003)
Podlubny, I., Fractional differential equations. Academic Press, San Diego, 1999
Samorodnitsky, G., Taqqu, M.S. Stable non-Gaussian random processes. Chapman and Hall, New York, 1994
Saxena, R.K., Mathai, A.M., Haubold, H.J., On generalized fractional kinetic equations. Physica A, 344:657–664 (2004)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhang, Sq. Solution of Semi-Boundless Mixed Problem for Time-fractional Telegraph Equation. Acta Mathematicae Applicatae Sinica, English Series 23, 611–618 (2007). https://doi.org/10.1007/s10255-007-0399
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s10255-007-0399
Keywords
- Time-fractional telegraph equation
- the Fourier sin and cos transforms
- mittag-leffler function
- H-function