Numerical Solution of Fractional Elliptic Problems with Inhomogeneous Boundary Conditions
Fractal 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
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Rational Spectral Methods for PDEs Involving Fractional Laplacian in Unbounded Domains [PDF]
SIAM Journal on Scientific Computing, 2019 Many PDEs involving fractional Laplacian are naturally set in unbounded domains with underlying solutions decay very slowly, subject to certain power laws. Their numerical solutions are under-explored.
T. Tang +3 more
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Path Laplacians versus fractional Laplacians as nonlocal operators on networks
New 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
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Mathematics, 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
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Bilevel optimization, deep learning and fractional Laplacian regularization with applications in tomography [PDF]
Inverse Problems, 2019 In this work we consider a generalized bilevel optimization framework for solving inverse problems. We introduce fractional Laplacian as a regularizer to improve the reconstruction quality, and compare it with the total variation regularization.
H. Antil, Z. Di, R. Khatri
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A fractional generalization of the classical lattice dynamics approach [PDF]
, 2016 We develop physically admissible lattice models in the harmonic approximation which define by Hamilton's variational principle fractional Laplacian matrices of the forms of power law matrix functions on the n-dimensional periodic and infinite lattice in ...
A.F. Nowakowski +33 more
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Solutions for nonhomogeneous fractional (p, q)-Laplacian systems with critical nonlinearities
Advances in Nonlinear Analysis, 2022 In this article, we aimed to study a class of nonhomogeneous fractional (p, q)-Laplacian systems with critical nonlinearities as well as critical Hardy nonlinearities in RN{{\mathbb{R}}}^{N}.
Tao Mengfei, Zhang Binlin
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Fast implicit difference schemes for time‐space fractional diffusion equations with the integral fractional Laplacian [PDF]
Mathematical methods in the applied sciences, 2020 In this paper, we develop two fast implicit difference schemes for solving a class of variable‐coefficient time–space fractional diffusion equations with integral fractional Laplacian (IFL).
Xianming Gu +3 more
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Fractional Laplacian system involving doubly critical nonlinearities in $\mathbb{R}^N$
Electronic Journal of Qualitative Theory of Differential Equations, 2017 In this article, we are interested in a fractional Laplacian system in $\mathbb{R}^N$, which involves critical Sobolev-type nonlinearities and critical Hardy–Sobolev-type nonlinearities.
Li Wang, Binlin Zhang, Haijin Zhang
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Existence of Multiple Weak Solutions to a Discrete Fractional Boundary Value Problem
Axioms, 2023 The existence of at least three weak solutions to a discrete fractional boundary value problem containing a p-Laplacian operator and subject to perturbations is proved using variational methods. Some applications of the main results are presented.
Shahin Moradi +2 more
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