Results 21 to 30 of about 33,455 (264)

On the Convergence Result of the Fractional Pseudoparabolic Equation

Journal of Mathematics, 2023
In this paper, we consider the nonlinear fractional Laplacian pseudoparabolic equation (NFLPPE). We mainly focus on the convergence of mild solutions with respect to the order of fractional Laplacian.
Nguyen Van Tien, Reza Saadati
doaj   +1 more source

Modeling Long-Distance Forward and Backward Diffusion Processes in Tracer Transport Using the Fractional Laplacian on Bounded Domains

Fractal and Fractional, 2023
Recent studies have emphasized the importance of the long-distance diffusion model in characterizing tracer transport occurring within both subsurface and surface environments, particularly in heterogeneous systems.
Zhipeng Li, Hongwu Tang, Saiyu Yuan, Huiming Zhang, Lingzhong Kong, HongGuang Sun   +5 more
doaj   +1 more source

Fractional N-Laplacian boundary value problems with jumping nonlinearities in the fractional Orlicz–Sobolev spaces

Boundary Value Problems, 2021
We investigate the multiplicity of solutions for problems involving the fractional N-Laplacian. We obtain three theorems depending on the source terms in which the nonlinearities cross some eigenvalues. We obtain these results by direct computations with
Q-Heung Choi, Tacksun Jung
doaj   +1 more source

A Monotone Discretization for the Fractional Obstacle Problem and Its Improved Policy Iteration

Fractal and Fractional, 2023
In recent years, the fractional Laplacian has attracted the attention of many researchers, the corresponding fractional obstacle problems have been widely applied in mathematical finance, particle systems, and elastic theory.
Rubing Han, Shuonan Wu, Hao Zhou
doaj   +1 more source

Asymmetric critical fractional p-Laplacian problems

Electronic Journal of Differential Equations, 2017
We consider the asymmetric critical fractional p-Laplacian problem $$\displaylines{ (-\Delta)^s_p u = \lambda |u|^{p-2} u + u^{p^\ast_s - 1}_+,\quad \text{in } \Omega;\cr u = 0, \quad \text{in } \mathbb{R}^N\setminus\Omega; }$$ where $\lambda>0 ...
Li Huang, Yang Yang
doaj   +2 more sources

A Generalized Fractional Laplacian

, 2023
In this article we show that the fractional Laplacian in $R^{2}$ can be factored into a product of the divergence operator, a Riesz potential operator, and the gradient operator. Using this factored form we introduce a generalization of the fractional Laplacian, involving a matrix $K(x)$, suitable when the fractional Laplacian is applied in a non ...
Zheng, Xiangcheng, Ervin, V. J., Wang, Hong   +2 more
openaire   +2 more sources

Fractional Laplacian in bounded domains [PDF]

Physical Review E, 2007
11 pages, 11 ...
Zoia, A., Rosso, A., Kardar, M.
openaire   +4 more sources

Monotone iterative technique for time-space fractional diffusion equations involving delay

Nonlinear Analysis, 2021
This paper considers the initial boundary value problem for the time-space fractional delayed diffusion equation with fractional Laplacian. By using the semigroup theory of operators and the monotone iterative technique, the existence and uniqueness of ...
Qiang Li, Guotao Wang, Mei Wei
doaj   +1 more source

Fractional Laplacians : A short survey

Discrete & Continuous Dynamical Systems - S, 2022
<p style='text-indent:20px;'>This paper describes the state of the art and gives a survey of the wide literature published in the last years on the fractional Laplacian. We will first recall some definitions of this operator in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^N $\end{document}</tex-math></inline-
Daoud, Maha, Laamri, El Haj
openaire   +2 more sources

A New Fifth-Order Finite Difference Compact Reconstruction Unequal-Sized WENO Scheme for Fractional Differential Equations

Fractal and Fractional, 2022
This paper designs a new finite difference compact reconstruction unequal-sized weighted essentially nonoscillatory scheme (CRUS-WENO) for solving fractional differential equations containing the fractional Laplacian operator.
Yan Zhang, Jun Zhu
doaj   +1 more source