Results 41 to 50 of about 101,180 (174)

Numerical Solution of Fractional Elliptic Problems with Inhomogeneous Boundary Conditions

open access: yesFractal and Fractional, 2021
The numerical solution of fractional-order elliptic problems is investigated in bounded domains. According to real-life situations, we assumed inhomogeneous boundary terms, while the underlying equations contain the full-space fractional Laplacian ...
Gábor Maros, Ferenc Izsák
doaj   +1 more source

The extremal solution for the fractional Laplacian [PDF]

open access: yesCalculus of Variations and Partial Differential Equations, 2013
We study the extremal solution for the problem $(- )^s u= f(u)$ in $ $, $u\equiv0$ in $\R^n\setminus $, where $ >0$ is a parameter and $s\in(0,1)$. We extend some well known results for the extremal solution when the operator is the Laplacian to this nonlocal case. For general convex nonlinearities we prove that the extremal solution is bounded
Ros Oton, Xavier   +1 more
openaire   +5 more sources

Existence and Uniqueness of Solutions to Four-Point Impulsive Fractional Differential Equations with p-Laplacian Operator

open access: yesMathematics, 2022
In this paper, by using fixed-point theorems, the existence and uniqueness of positive solutions to a class of four-point impulsive fractional differential equations with p-Laplacian operators are studied. In addition, three examples are given to justify
Limin Chu   +3 more
doaj   +1 more source

Path Laplacians versus fractional Laplacians as nonlocal operators on networks

open access: yesNew Journal of Physics, 2021
Here we study and compare nonlocal diffusion processes on networks based on two different kinds of Laplacian operators. We prove that a nonlocal diffusion process on a network based on the path Laplacian operator always converges faster than the standard
Ernesto Estrada
doaj   +1 more source

Fractional Laplacian in conformal geometry [PDF]

open access: yesAdvances in Mathematics, 2011
In this note, we study the connection between the fractional Laplacian operator that appeared in the recent work of Caffarelli-Silvestre and a class of conformally covariant operators in conformal geometry.
González Nogueras, María del Mar   +1 more
openaire   +5 more sources

Remarks on the Generalized Fractional Laplacian Operator

open access: yesMathematics, 2019
The fractional Laplacian, also known as the Riesz fractional derivative operator, describes an unusual diffusion process due to random displacements executed by jumpers that are able to walk to neighbouring or nearby sites, as well as perform excursions ...
Chenkuan Li   +3 more
doaj   +1 more source

A comparative study on nonlocal diffusion operators related to the fractional Laplacian [PDF]

open access: yesDiscrete and Continuous Dynamical Systems B, 24 (2019), pp. 231-256, 2017
In this paper, we study four nonlocal diffusion operators, including the fractional Laplacian, spectral fractional Laplacian, regional fractional Laplacian, and peridynamic operator. These operators represent the infinitesimal generators of different stochastic processes, and especially their differences on a bounded domain are significant.
arxiv   +1 more source

Transference of Fractional Laplacian Regularity [PDF]

open access: yes, 2014
In this note we show how to obtain regularity estimates for the fractional Laplacian on the multidimensional torus $\mathbb{T}^n$ from the fractional Laplacian on $\mathbb{R}^n$. Though at first glance this may seem quite natural, it must be carefully precised. A reason for that is the simple fact that $L^2$ functions on the torus can not be identified
Roncal, L., Stinga, P.R.
openaire   +4 more sources

Mellin definition of the fractional Laplacian

open access: yesFractional Calculus and Applied Analysis, 2023
It is known that at least ten equivalent definitions of the fractional Laplacian exist in an unbounded domain. Here we derive a further equivalent definition that is based on the Mellin transform and it can be used when the fractional Laplacian is applied to radial functions.
Gianni Pagnini, Claudio Runfola
openaire   +3 more sources

Variational Inequalities for the Fractional Laplacian [PDF]

open access: yesPotential Analysis, 2016
19 ...
MUSINA, Roberta   +2 more
openaire   +4 more sources

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