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pro vyhledávání: '"26a33"'
The definition of generalized random processes in Gel'fand sense allows to extend well-known stochastic models, such as the fractional Brownian motion, and study the related fractional pde's, as well as stochastic differential equations in distributi
Externí odkaz:
http://arxiv.org/abs/2410.22880
Autor:
Haardt, Luca, Tolksdorf, Patrick
We establish the Kato square root property for the generalized Stokes operator on $\mathbb{R}^d$ with bounded measurable coefficients. More precisely, we identify the domain of the square root of $Au := - \operatorname{div}(\mu \nabla u) + \nabla \ph
Externí odkaz:
http://arxiv.org/abs/2410.18787
We study the second-order asymptotic expansion of the $s$-fractional Gagliardo seminorm as $s\to1^-$ in terms of a higher order nonlocal functional. We prove a Mosco-convergence result for the energy functionals and that the $L^2$-gradient flows of t
Externí odkaz:
http://arxiv.org/abs/2410.17829
Autor:
Thai, H. D., Tuan, H. T.
This paper systematically treats the asymptotic behavior of many (linear/nonlinear) classes of higher-order fractional differential equations with multiple terms. To do this, we utilize the characteristics of Caputo fractional differentiable function
Externí odkaz:
http://arxiv.org/abs/2410.09369
Autor:
Amaonyeiro, Anslem, Egwe, Murphy E
This paper considers a new version of fractional Sobolev spaces $\widetilde{\mathcal{W}}_{\mathcal{U}}^{\beta,p}(\mathbb{C}^{n})$ defined using the concept of tempered ultradistributions with respect to the spaces of ultradifferentiable functions $\m
Externí odkaz:
http://arxiv.org/abs/2410.09074
Autor:
Crider, Sarah M., Hillstrom, Shawn
An incomplete Riemann zeta function can be expressed as a lower-bounded, improper Riemann-Liouville fractional integral, which, when evaluated at $0$, is equivalent to the complete Riemann zeta function. Solutions to Landau's problem with $\zeta(s) =
Externí odkaz:
http://arxiv.org/abs/2410.01069
In this manuscript, we extend our previous work on the Riemann-Liouville fractional integral of order $\alpha > 0$ in Bochner-Lebesgue spaces. We specifically address the remaining cases concerning its boundedness when $\alpha > 1/p$. Furthermore, we
Externí odkaz:
http://arxiv.org/abs/2410.00830
In this paper, we focus on the functional and geometrical aspects of the fractional Sobolev capacity, the Besov capacity and the Riesz capacity on stratified lie groups, respectively. Firstly, we provide a new Carleson characterization of the extensi
Externí odkaz:
http://arxiv.org/abs/2409.18720
Autor:
Salgado, Abner J., Sawyer, Shane E.
We present a technique for approximating solutions to the spectral fractional Laplacian, which is based on the Caffarelli-Silvestre extension and diagonalization. Our scheme uses the analytic solution to the associated eigenvalue problem in the exten
Externí odkaz:
http://arxiv.org/abs/2409.17388
Autor:
Bhalekar, Sachin, Dutta, Pragati
The differential equations involving two discrete delays are helpful in modeling two different processes in one model. We provide the stability and bifurcation analysis in the fractional order delay differential equation $D^\alpha x(t)=a x(t)+b x(t-\
Externí odkaz:
http://arxiv.org/abs/2409.15772