Numerical approximation of the integral fractional Laplacian [PDF]
Numerische Mathematik, 2019 We propose a new nonconforming finite element algorithm to approximate the solution to the elliptic problem involving the fractional Laplacian. We first derive an integral representation of the bilinear form corresponding to the variational problem. The numerical approximation of the action of the corresponding stiffness matrix consists of three steps:
Andrea Bonito +2 more
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The Brezis-Nirenberg problem for the fractional p-Laplacian [PDF]
, 2016 We obtain nontrivial solutions to the Brezis–Nirenberg problem for the fractional p-Laplacian operator, extending some results in the literature for the fractional Laplacian.
Squassina, Marco
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Nontrivial Solution for the Fractional p-Laplacian Equations via Perturbation Methods
Advances in Mathematical Physics, 2017 We study the existence of nontrivial solution of the following equation without compactness: (-Δ)pαu+up-2u=f(x,u), x∈RN, where N,p≥2, α∈(0,1), (-Δ)pα is the fractional p-Laplacian, and the subcritical p-superlinear term f∈C(RN×R) is 1-periodic in xi ...
Huxiao Luo, Shengjun Li, Xianhua Tang
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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 Supercritical Killings
Communications in Mathematical PhysicsIn this paper, we study Feynman-Kac semigroups of symmetric $α$-stable processes with supercritical killing potentials belonging to a large class of functions containing functions of the form $b|x|^{-β}$, where $b>0$ and $β>α$. We obtain two-sided estimates on the densities $p(t, x, y)$ of these semigroups for all $t>0$, along with estimates ...
Soobin Cho, Renming Song
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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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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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Fractional Laplacian matrix on the finite periodic linear chain and its periodic Riesz fractional derivative continuum limit: Discrete and continuous fractional Laplacian on finite periodic chain. [PDF]
, 2015 International audienceThe 1D discrete fractional Laplacian operator on a cyclically closed (periodic) linear chain with finite number $N$ of identical particles is introduced.
Nowakowski, Andrzej, +3 more
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Sub-fractional Brownian motion and its relation to occupation times [PDF]
We study a long-range dependence Gaussian process which we call “sub-fractional Brownian motion” (sub-fBm), because it is intermediate between Brownian motion (Bm) and fractional Brownian motion (fBm) in the sense that it has properties analogous to ...
Luis G. Gorostiza +2 more
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On (Global) unique continuation properties of the fractional discrete Laplacian [PDF]
We study various qualitative and quantitative (global) unique continuation properties for the fractional discrete Laplacian. We show that while the fractional Laplacian enjoys striking rigidity properties in the form of (global) unique continuation ...
Fernández Bertolin, Aingeru +2 more
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