Hardy—Littlewood—Sobolev Inequalities with the Fractional Poisson Kernel and Their Applications in PDEs
Sign Up to like & getrecommendations! Published in 2019 at "Acta Mathematica Sinica, English Series"
DOI: 10.1007/s10114-019-8417-2
Abstract: The purpose of this paper is five-fold. First, we employ the harmonic analysis techniques to establish the following Hardy-Littlewood-Sobolev inequality with the fractional Poisson kernel on the upper half space $$\int_{\mathbb{R}_ + ^n} {{{\int_{\partial \mathbb{R}_… read more here.
Keywords: fractional poisson; hardy littlewood; mathbb; littlewood sobolev ... See more keywords
A Semigroup Approach to Fractional Poisson Processes
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DOI: 10.1007/s11785-018-0763-z
Abstract: It is well-known that fractional Poisson processes (FPP) constitute an important example of a non-Markovian structure. That is, the FPP has no Markov semigroup associated via the customary Chapman–Kolmogorov equation. This is physically interpreted as… read more here.
Keywords: banach space; alpha alpha; poisson processes; semigroup approach ... See more keywords
Non-homogeneous space-time fractional Poisson processes
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DOI: 10.1080/07362994.2018.1541749
Abstract: Abstract The space-time fractional Poisson process (STFPP), defined by Orsingher and Poilto (2012), is a generalization of the time fractional Poisson process (TFPP) and the space fractional Poisson process (SFPP). We study the fractional generalization… read more here.
Keywords: time fractional; poisson; poisson process; process ... See more keywords
Tempered fractional Poisson processes and fractional equations with Z-transform
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DOI: 10.1080/07362994.2020.1748056
Abstract: Abstract In this article, we derive the state probabilities of different type of space- and time-fractional Poisson processes using z-transform. We work on tempered versions of time-fractional Poisson process and space-fractional Poisson processes. We also… read more here.
Keywords: poisson processes; tempered fractional; fractional equations; poisson ... See more keywords
Block-pulse functions method for solving three-dimensional fractional Poisson type equations with Neumann boundary conditions
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DOI: 10.1186/s13661-018-0945-7
Abstract: In this paper, a numerical scheme based on the three-dimensional block-pulse functions is proposed to solve the three-dimensional fractional Poisson type equations with Neumann boundary conditions. The differential operational matrices of fractional order of the… read more here.
Keywords: three dimensional; pulse functions; block pulse; poisson type ... See more keywords