Results 101 to 110 of about 5,262 (196)

The Dirichlet problem for the fractional Laplacian [PDF]

The main object under study in this thesis is the fractional Laplacian. In this work, we review the proof of existence and uniqueness of weak solutions to the Dirichlet problem for this operator. We also prove that such weak solutions are in fact smooth,
Burón i Palau, Antoni
core   +2 more sources

On Shape Optimization Theory With Fractional p-Laplacian Operators

Abstract and Applied Analysis
The focus of this paper is the investigation of shape optimization problems with operators such as fractional Laplacian and p-Laplacian operators, that is, −Δs and −Δps, where ...
Malick Fall, Alassane Sy, Ibrahima Faye, Diaraf Seck   +3 more
doaj   +1 more source

Mild solutions to Love-type equations on R^2

Electronic Journal of Differential Equations
In this article, we study a non-local Love problem on unbounded domains where the non-locality in the main equation is interpreted as a fractional Laplacian operator.
Bui Duc Nam, Bui Dai Nghia, Nguyen Anh Tuan   +2 more
doaj  

A finite-volume scheme for fractional diffusion on bounded domains

European Journal of Applied Mathematics
We propose a new fractional Laplacian for bounded domains, expressed as a conservation law and thus particularly suited to finite-volume schemes. Our approach permits the direct prescription of no-flux boundary conditions.
Rafael Bailo, José A. Carrillo, Stefano Fronzoni, David Gómez-Castro   +3 more
doaj   +1 more source

Higher differentiability for the fractional p-Laplacian

Mathematische Annalen
Abstract In this work, we study the higher differentiability of solutions to the inhomogeneous fractional p-Laplace equation under different regularity assumptions on the data. In the superquadratic case, we extend and sharpen several previous results, while in the subquadratic regime our results constitute completely novel developments even ...
Diening, Lars, Kim, Kyeongbae, Lee, Ho-Sik, Nowak, Simon Noah   +3 more
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New Results for p-Laplacian Fractional Instantaneous and Noninstantaneous Impulsive Differential Equations

Journal of Function Spaces
The p-Laplacian fractional differential equations have been studied extensively because of their numerous applications in science and engineering.
Wangjin Yao, Huiping Zhang
doaj   +1 more source

Null controllability from the exterior of fractional parabolic-elliptic coupled systems

Electronic Journal of Differential Equations, 2020
We analyze the null controllability properties from the exterior of two parabolic-elliptic coupled systems governed by the fractional Laplacian $(-d_x^2)^s$, $s\in(0,1)$, in one space dimension.
Carole Louis-Rose
doaj  

Minimizing eigenvalues of the fractional Laplacian

Calculus of Variations and Partial Differential Equations
Abstract We study the minimizers of $$\lambda _k^s(A) + |A|$$ λ k s
openaire   +2 more sources

Numerical Treatment of Stochastic Dynamic Systems with Fractional Laplacian Terms [PDF]

, 2019
The fractional Laplacian is an integro-differential operator that is currently widely used in nonlocal models, such as the anomalous diffusion, which arises when a particle moves randomly in the space involving a random process that allows long jumps ...
Jiao, Yiyu
core  

Existence Results for $\aleph$-Caputo Fractional Boundary Value Problems with $p$-Laplacian Operator

Journal of New Theory
This study delves into the investigation of positive solutions for a specific class of $\aleph$-Caputo fractional boundary value problems with the inclusion of the p-Laplacian operator. In this research, we use the theory of the fixed point theory within
Özlem Batit Özen
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