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Laplace-Laplace analysis of the fractional Poisson process
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In this article, the fractional Poisson process was generated by subordinating the standard Poisson processes to the inverse stable subordinator, based on application of the Laplace transform with respect to both arguments of the evolving probability densities.Abstract:
We generate the fractional Poisson process by subordinating the standard Poisson process to the inverse stable subordinator. Our analysis is based on application of the Laplace transform with respect to both arguments of the evolving probability densities.read more
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Book ChapterDOI
Multi-index Mittag-Leffler Functions
TL;DR: In this paper, Dzherbashian [Dzh60] defined a function with positive α 1 > 0, α 2 > 0 and real α 1, β 2, β 3, β 4, β 5, β 6, β 7, β 8, β 9, β 10, β 11, β 12, β 13, β 14, β 15, β 16, β 17, β 18, β 20, β 21, β 22, β 24
Journal ArticleDOI
Hilfer–Prabhakar derivatives and some applications
TL;DR: A generalization of Hilfer derivatives in which Riemann–Liouville integrals are replaced by more general Prabhakar integrals is presented, which shows some applications in classical equations of mathematical physics such as the heat and the free electron laser equations.
The Fractional Poisson Process and the Inverse Stable Subordinator
Ear,Nih grant R Eb +1 more
TL;DR: In this paper, 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.
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The Classical Mittag-Leffler Function
TL;DR: In this article, the basic properties of the classical Mittag-Leffler function E α (z) are presented, and the material can be formally divided into two parts.
References
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Book
Theory and Applications of Fractional Differential Equations
TL;DR: In this article, the authors present a method for solving Fractional Differential Equations (DFE) using Integral Transform Methods for Explicit Solutions to FractionAL Differentially Equations.
Journal ArticleDOI
Random Walks on Lattices. II
TL;DR: In this paper, the mean first passage times and their dispersion in random walks from the origin to an arbitrary lattice point on a periodic space lattice with periodic boundary conditions have been derived by the method of Green's functions.
Book
The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type
TL;DR: In this paper, the existence and uniqueness results for Riemann-Liouville Fractional Differential Equations are presented. But they do not cover the special cases of fractional calculus.