Chapter for Handbook of Fractional Calculus with Applications
نویسندگان
چکیده
The inverse stable subordinator is the first passage time of a standard stable subordinator with index 0 < β < 1. The probability density of the inverse stable subordinator can be used to solve time-fractional Cauchy problems, where the usual first derivative in time is replaced by a Caputo fractional derivative of order β. If the Cauchyproblemgoverns aMarkov process, then the fractional Cauchy problemgoverns a time-changedprocess, where the timeparameter is replaced by the inverse stable subordinator. Applications include delayed Brownian motion, and the fractional Poisson process.
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