arXiv subjects
Publications and source records attributed to Jung Hun Han.
Fractional renewal processes as a generalization of Poisson process are already in the literature. In this paper, by introducing a new concept of generalized density function, the authors construct new fractional renewal processes in the $α$-fractional space and show that it is another interesting and useful generalization of Poisson process.
In this paper, we introduce the Levy density function as the limit of a generalized Mittag-Leffler density function. The fractional integral equation for the generalized Mittag-Leffler density function is also given. And the role of the Levy structure in the fractional calculus is described. Finally, a transformation is defined.
In this paper, we show new representations of one-sided Lévy stable distributions for irrational Lévy indices of the type $\left(\frac{p}{q}\right)^{\frac{l_{2}}{l_{1}}}$ which are not covered in \cite{pg1} : for rational Lévy indices. Furthermore, other equivalent representations for a distribution of a rational Lévy index is described. We also give a simplest proof for the formulae which cover the cases for rational Lévy indices. Finally we introduce the concepts of Lévy smashing and Lévy-smashed gamma stochastic processes.