Results 11 to 20 of about 1,534 (121)

Fractional Fokker-Planck-Kolmogorov type Equations and their Associated Stochastic Differential Equations [PDF]

, 2011
MSC 2010: 26A33, 35R11, 35R60, 35Q84, 60H10 Dedicated to 80-th anniversary of Professor Rudolf GorenfloThere is a well-known relationship between the Itô stochastic differential equations (SDEs) and the associated partial differential equations called ...
Hahn, Marjorie, Umarov, Sabir
core   +1 more source

A preconditioned iterative method for coupled fractional partial differential equation in European option pricing

Open Mathematics, 2023
Recently, regime-switching option pricing based on fractional diffusion models has been used, which explains many significant empirical facts about financial markets better.
Wu Shuang, Chou Lot-Kei, Chen Xu, Lei Siu-Long   +3 more
doaj   +1 more source

Regularity and Bernstein-type results for nonlocal minimal surfaces [PDF]

, 2013
We prove that, in every dimension, Lipschitz nonlocal minimal surfaces are smooth. Also, we extend to the nonlocal setting a famous theorem of De Giorgi stating that the validity of Bernstein's theorem in dimension $n+1$ is a consequence of the ...
Figalli, Alessio, Valdinoci, Enrico
core   +4 more sources

A posteriori error estimates based on superconvergence of FEM for fractional evolution equations

Open Mathematics, 2021
In this paper, we consider an approximation scheme for fractional evolution equation with variable coefficient. The space derivative is approximated by triangular finite element and the time fractional derivative is evaluated by the L1 approximation. The
Tang Yuelong, Hua Yuchun
doaj   +1 more source

Existence of Ground States of Fractional Schrödinger Equations

Advanced Nonlinear Studies, 2021
We consider ground states of the nonlinear fractional Schrödinger equation with ...
Ma Li, Li Zhenxiong
doaj   +1 more source

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
doaj   +1 more source

Rational approximation to the fractional Laplacian operator in reaction-diffusion problems [PDF]

, 2016
This paper provides a new numerical strategy to solve fractional in space reaction-diffusion equations on bounded domains under homogeneous Dirichlet boundary conditions.
Aceto, Lidia, Novati, Paolo
core   +3 more sources

Equivalence between a time-fractional and an integer-order gradient flow: The memory effect reflected in the energy

Advances in Nonlinear Analysis, 2022
Time-fractional partial differential equations are nonlocal-in-time and show an innate memory effect. Previously, examples like the time-fractional Cahn-Hilliard and Fokker-Planck equations have been studied.
Fritz Marvin, Khristenko Ustim, Wohlmuth Barbara   +2 more
doaj   +1 more source

Some remarks on the duality method for Integro-Differential equations with measure data [PDF]

, 2015
We deal with existence, uniqueness, and regularity for solutions of the boundary value problem $$ \begin{cases} {\mathcal L}^s u = \mu &\quad \text{in $\Omega$}, u(x)=0 \quad &\text{on} \ \ \mathbb{R}^N\backslash\Omega, \end{cases} $$ where $\Omega$ is
Petitta, Francesco
core   +1 more source

Multiplicity solutions of a class fractional Schrödinger equations

Open Mathematics, 2017
In this paper, we study the existence of nontrivial solutions to a class fractional Schrödinger equations (−Δ)su+V(x)u=λf(x,u)inRN, $$ {( - \Delta )^s}u + V(x)u = \lambda f(x,u)\,\,{\rm in}\,\,{\mathbb{R}^N}, $$ where (−Δ)su(x)=2limε→0∫RN∖Bε(X)u(x)−u(y ...
Jia Li-Jiang, Ge Bin, Cui Ying-Xin, Sun Liang-Liang   +3 more
doaj   +1 more source