217 citations · 1.1k across the 56 of their papers we have counts for
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Strong analytic solutions of fractional Cauchy problems
Jebessa B. Mijena, Erkan Nane
Fractional derivatives can be used to model time delays in a diffusion process. When the order of the fractional derivative is distributed over the unit interval, it is useful for…
Space-time fractional diffusion on bounded domains
Zhen-Qing Chen, Mark M. Meerschaert, Erkan Nane
Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. T…
Time-Changed Poisson Processes
A. Kumar, Erkan Nane, P. Vellaisamy
We consider time-changed Poisson processes, and derive the governing difference-differential equations (DDE) these processes. In particular, we consider the time-changed Poisson pr…
Interacting time-fractional and PDEs systems via Brownian-time and Inverse-stable-Lévy-time Brownian sheets
Hassan Allouba, Erkan Nane
Lately, many phenomena in both applied and abstract mathematics and related disciplines have been expressed in terms of high order and fractional PDEs. Recently, Allouba introduced…
Fractal Dimensions for Continuous Time Random Walk Limits
Mark M. Meerschaert, Erkan Nane, Yimin Xiao
In a continuous time random walk (CTRW), each random jump follows a random waiting time. CTRW scaling limits are time-changed processes that model anomalous diffusion. The outer pr…