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math.PR2010★ 2 cited
The fractional Poisson process and the inverse stable subordinator
Mark M. Meerschaert, Erkan Nane, P. Vellaisamy
The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its distributions solve a time-fractional analogue of the Kolmogorov forward equation for a P…
math.PR2010
Transient anomalous sub-diffusion on bounded domains
Erkan Nane, Mark M. Meerschaert, Palaniappan Vellaisamy
This paper develops strong solutions and stochastic solutions for the tempered fractional diffusion equation on bounded domains. First the eigenvalue problem for tempered fractiona…