Results 81 to 90 of about 101,180 (174)
Fractional Laplacian matrix on the finite periodic linear chain and its periodic Riesz fractional derivative continuum limit [PDF]
arXiv, 2014 The 1D discrete fractional Laplacian operator on a cyclically closed (periodic) linear chain with finitenumber $N$ of identical particles is introduced. We suggest a "fractional elastic harmonic potential", and obtain the $N$-periodic fractionalLaplacian operator in the form of a power law matrix function for the finite chain ($N$ arbitrary not ...
arxiv
The fractional Laplacian: a primer
, 2023 In this note we give a glimpse of the fractional Laplacian. In particular, we bring several definitions of this non-local operator and series of proofs of its properties. It is structured in a way as to show that several of those properties are natural extensions of their local counterparts, with some key differences.
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A Liouville Theorem for the Fractional Laplacian [PDF]
arXiv, 2014 We extend the classical Liouville Theorem from Laplacian to the fractional Laplacian, that is, we prove Every $\alpha$-harmonic function bounded either above or below in all of $R^n$ must be constant.
arxiv
Discrete Laplacian Operator and Its Applications in Signal Processing
IEEE Access, 2020 Fractional calculus has increased in popularity in recent years, as the number of its applications in different fields has increased. Compared to the traditional operations in calculus (integration and differentiation) which are uniquely defined, the ...
Waseem Waheed, Guang Deng, Bo Liu
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Fractional Laplacian with singular drift [PDF]
Studia Mathematica, 2011 For $ \in (1,2)$ we consider the equation $\partial_t u = ^{ /2} u - r b \cdot \nabla u$, where $b$ is a divergence free singular vector field not necessarily belonging to the Kato class. We show that for sufficiently small $r>0$ the fundamental solution is globally in time comparable with the density of the isotropic stable ...
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On a coupled system of fractional sum-difference equations with p-Laplacian operator
Advances in Difference Equations, 2020 In this paper, we propose a nonlocal fractional sum-difference boundary value problem for a coupled system of fractional sum-difference equations with p-Laplacian operator. The problem contains both Riemann–Liouville and Caputo fractional difference with
Pimchana Siricharuanun +2 more
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Positive Solution for the Nonlinear Hadamard Type Fractional Differential Equation with p-Laplacian
Journal of Function Spaces and Applications, 2013 We study the following nonlinear fractional differential equation involving the p-Laplacian operator DβφpDαut=ft,ut ...
Ya-ling Li, Shi-you Lin
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Spectral Asymptotics for Fractional Laplacians [PDF]
, 2019 In this article we consider fractional Laplacians which seem to be of interest to probability theory. This is a rather new class of operators for us but our methods works (with a twist, as usual). Our main goal is to derive a two-term asymptotics as one-term asymptotics is easily obtained by R.~Seeley's method.
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On fractional $p$-Laplacian problems with weight
Differential and Integral Equations, 2015 10 ...
Lehrer, R., Maia, L., Squassina, Marco
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Resolvent kernel for the Kohn Laplacian on Heisenberg groups
Electronic Journal of Differential Equations, 2002 We present a formula that relates the Kohn Laplacian on Heisenberg groups and the magnetic Laplacian. Then we obtain the resolvent kernel for the Kohn Laplacian and find its spectral density.
Neur Eddine Askour, Zouhair Mouayn
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