THE SPACE-FRACTIONAL TELEGRAPH EQUATION AND THE RELATED FRACTIONAL TELEGRAPH PROCESS

Citation:

E. ORSINGHER,ZHAO Xuelei.THE SPACE-FRACTIONAL TELEGRAPH EQUATION AND THE RELATED FRACTIONAL TELEGRAPH PROCESS[J].Chinese Annals of Mathematics B,2003,24(1):45~56
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Authors:

E. ORSINGHER; ZHAO Xuelei

Foundation:

Project supported by the National Natural Science Foundation of China (No. 10071014).
Abstract: The space-fractional telegraph equation is analyzed and the Fourier transform of its fundamental solution is obtained and discussed. A symmetric process with discontinuous trajectories, whose transition function satisfies the space-fractional telegraph equation, is presented. Its limiting behaviour and the connection with symmetric stable processes is also examined.

Keywords:

Fractional calculus, Marchaud’s derivative, Weyl’s derivative, Riesz potential, Telegraph equation, Stable processes

Classification:

60H30, 35G05
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