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Erkan Nane
Researcher at Auburn University
Publications - 120
Citations - 2276
Erkan Nane is an academic researcher from Auburn University. The author has contributed to research in topics: Fractional calculus & Subordinator. The author has an hindex of 23, co-authored 113 publications receiving 1989 citations. Previous affiliations of Erkan Nane include Purdue University & Michigan State University.
Papers
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The Fractional Poisson Process and the Inverse Stable Subordinator
TL;DR: In this article, it was shown that a traditional Poisson process, with the time variable replaced by an independent inverse stable subordinator, is also a fractional poisson process with Mittag-Leffler waiting times, which unifies the two main approaches in stochastic theory of time-fractional diffusion equations.
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Fractional Cauchy problems on bounded domains
TL;DR: In this paper, Meerschaert et al. extended the approach of Meershaert and Scheffler (23) to fractional Cauchy problems on bounded domains and constructed stochastic solutions via an inverse stable subordi- nator whose scaling index corresponds to the order of the fractional time derivative.
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Distributed-order fractional diffusions on bounded domains
TL;DR: In this article, strong solutions and stochastic analogues for distributed-order time-fractional diffusion equations on bounded domains, with Dirichlet boundary conditions, were provided.
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Space-time fractional diffusion on bounded domains
TL;DR: In this article, the authors develop strong solutions of space-time fractional diffusion equations on bounded domains, as well as probabilistic representations of these solutions, which are useful for particle tracking codes.
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Brownian subordinators and fractional Cauchy problems
TL;DR: In this article, the scaling limits of continuous time random walks were shown to be equivalent to the hitting time process of a classical stable subordinator, and a close and unexpected connection between these two classes of processes and an equivalence between two families of partial differential equations.