Annales Mathematicae Silesianae, 2020 This work presents a numerical comparison between two efficient methods namely the fractional natural variational iteration method (FNVIM) and the fractional natural homotopy perturbation method (FNHPM) to solve a certain type of nonlinear Caputo time ...
Khalouta Ali, Kadem Abdelouahab
doaj +1 more source
Space-time duality for semi-fractional diffusions [PDF]
Fractal Geometry and Stochastics VI, Progress in Probability 76,
2021, pp. 255-272, 2019 Almost sixty years ago Zolotarev proved a duality result which relates an $\alpha$-stable density for $\alpha\in(1,2)$ to the density of a $\frac1{\alpha}$-stable distribution on the positive real line. In recent years Zolotarev duality was the key to show space-time duality for fractional diffusions stating that certain heat-type fractional equations ...
arxiv
Uniqueness for fractional parabolic and elliptic equations with drift [PDF]
arXiv, 2022 We investigate uniqueness, in suitable weighted Lebesgue spaces, of solutions to a class of fractional parabolic and elliptic equations with a drift.
arxiv
Ground-state solutions for fractional Kirchhoff-Choquard equations with critical growth
Advances in Nonlinear AnalysisWe study the following fractional Kirchhoff-Choquard equation: a+b∫RN(−Δ)s2u2dx(−Δ)su+V(x)u=(Iμ*F(u))f(u),x∈RN,u∈Hs(RN),\left\{\begin{array}{l}\left(a+b\mathop{\displaystyle \int }\limits_{{{\mathbb{R}}}^{N}}{\left|{\left(-\Delta )}^{\frac{s}{2}}u\right|}
Yang Jie, Chen Haibo
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Solvability and microlocal analysis of the fractional Eringen wave equation
, 2017 We discuss unique existence and microlocal regularity properties of Sobolev space solutions to the fractional Eringen wave equation, initially given in the form of a system of equations in which the classical non-local Eringen constitutive equation is ...
Hörmann, Günther +2 more
core +1 more source
On a space discretization scheme for the Fractional Stochastic Heat Equations [PDF]
arXiv, 2011 In this work, we introduce a new discretization to the fractional Laplacian and use it to elaborate an approximation scheme for fractional heat equations perturbed by a multiplicative cylindrical white noise. In particular, we estimate the rate of convergence.
arxiv
Fractional Calculus of Variations for Double Integrals [PDF]
, 2011 We consider fractional isoperimetric problems of calculus of variations with double integrals via the recent modified Riemann-Liouville approach. A necessary optimality condition of Euler-Lagrange type, in the form of a multitime fractional PDE, is ...
Odzijewicz, Tatiana +1 more
core +3 more sources
Well-posedness for the Cauchy problem for a fractional porous medium equation with variable density in one space dimension [PDF]
arXiv, 2012 We study existence and uniqueness of bounded solutions to a fractional nonlinear porous medium equation with a variable density, in one space dimension.
arxiv
Optimal rearrangement problem and normalized obstacle problem in the fractional setting
Advances in Nonlinear Analysis, 2020 We consider an optimal rearrangement minimization problem involving the fractional Laplace operator (–Δ)s, 0 < s < 1, and the Gagliardo seminorm |u|s. We prove the existence of the unique minimizer, analyze its properties as well as derive the non-local ...
Bonder Julián Fernández +2 more
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Non-critical dimensions for critical problems involving fractional Laplacians [PDF]
arXiv, 2013 We study the Brezis--Nirenberg effect in two families of noncompact boundary value problems involving Dirichlet-Laplacian of arbitrary real order $m>0$.
arxiv