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pro vyhledávání: '"Nane, Erkan"'
Autor:
Guerngar, Ngartelbaye, Nane, Erkan
We study the space-time nonlinear fractional stochastic heat equation driven by a space-time white noise, \begin{align*} \partial_t^\beta u(t,x)=-(-\Delta)^{\alpha/2}u(t,x)+I_t^{1-\beta}\Big[\sigma(u(t,x))\dot{W}(t,x)\Big],\ \ t>0, \ x\in \mathbb{R}
Externí odkaz:
http://arxiv.org/abs/2403.01379
The finite time blowup in the almost sure sense of a class of space-time fractional stochastic partial differential equations is discussed. Both the cases of white noise and colored noise are considered. The sufficient and necessary condition between
Externí odkaz:
http://arxiv.org/abs/2202.11564
In this paper we study the long time behavior of the solution to a certain class of space-time fractional stochastic equations with respect to the level $\lambda$ of a noise and show how the choice of the order $\beta \in (0, \,1)$ of the fractional
Externí odkaz:
http://arxiv.org/abs/2110.09475
We consider a class of nonlinear fractional equations having the Caputo fractional derivative of the time variable $t$, the fractional order of the self-adjoint positive definite unbounded operator in a Hilbert space and a singular nonlinear source.
Externí odkaz:
http://arxiv.org/abs/2002.06747
The blowup in finite time of solutions to SPDEs \begin{equation*} \partial_tu_t(x)=-\phi(-\Delta)u_t(x) +\sigma(u_t(x))\dot{\xi}(t,x), \quad t>0,x\in\mathbb{R}^d, \end{equation*} { is} investigated, where $\dot{\xi}$ could be either a white noise or
Externí odkaz:
http://arxiv.org/abs/2001.00320
Autor:
Guerngar, Ngartelbaye, Nane, Erkan, Tinatztepe, Ramazan, Ulusoy, Suleyman, Van Wyk, Hans Werner
In this article, we consider the space-time fractional (nonlocal) equation characterizing the so-called "double-scale" anomalous diffusion $$\partial_t^\beta u(t, x) = -(-\Delta)^{\alpha/2}u(t,x) - (-\Delta)^{\gamma/2}u(t,x) \ \ t> 0, \ -1
Externí odkaz:
http://arxiv.org/abs/1912.01779
Publikováno v:
In Bulletin des sciences mathématiques December 2023 189
Consider the following class of conformable time-fractional stochastic equation $$T_{\alpha,t}^a u(x,t)=\lambda\sigma(u(x,t))\dot{W}_t,\,\,\,\,x\in\mathbb{R},\,t\in[a,\infty), \,\,0<\alpha<1,$$ with a non-random initial condition $u(x,0)=u_0(x),\,x\i
Externí odkaz:
http://arxiv.org/abs/1907.08146
Autor:
Nane, Erkan, Ni, Yinan
This paper studies a time-changed stochastic control problem, where the underlying stochastic process is a L\'evy noise time-changed by an inverse subordinator. We establish a maximum principle theory for the time-changed stochastic control problem.
Externí odkaz:
http://arxiv.org/abs/1905.11921
Autor:
Meng, Xiangqian, Nane, Erkan
Publikováno v:
Fract. Calc. Appl. Anal. Vol. 23, No 1 (2020), pp. 224-249
We consider non-linear time-fractional stochastic heat type equation $$\frac{\partial^\beta u}{\partial t^\beta}+\nu(-\Delta)^{\alpha/2} u=I^{1-\beta}_t \bigg[\int_{\mathbb{R}^d}\sigma(u(t,x),h) \stackrel{\cdot}{\tilde N }(t,x,h)\bigg]$$ and $$\frac{
Externí odkaz:
http://arxiv.org/abs/1902.10637