Abstract :
We investigate several aspects of the fractional telegraph equations, in an effort to better
understand the anomalous diffusion processes observed in blood flow experiments. In the
earlier work Eckstein et al. [Electron. J. Differential Equations Conf. 03 (1999) 39–50],
the telegraph equation D2u + 2aDu + Au = 0 was used, where D = d/dt, and it was
shown that, as t tends to infinity, u is approximated by v, where 2aDv + Av = 0; here
A = −d2/dx2 on L2(R), or A can be a more general nonnegative selfadjoint operator.
In this paper the concern is with the fractional telegraph equation E2u+ 2aEu + Au = 0,
where E = Dγ and 0<γ <1; after solving this equation it is shown that u is approximated
by v, where 2aEv + Av = 0.
2002 Elsevier Science (USA). All rights reserved.
