RT journal article
T1 Maximal regularity in ℓp spaces for discrete time fractional shifted equations
A1 Lizama, Carlos
A1 Murillo Arcila, Marina
A2 Matemáticas
K1 Maximal $\ell_p$-regularity
K1 shifted equations
K1 discrete time
K1 Gr\"unwald-Letnikov derivative
AB In this paper, we are presenting a new method based on operator-valued Fourier multipliers to \- characterize the existence and uniqueness of $\ell_p$-solutions for discrete time fractional models in the form$$ \Delta^{\alpha}u(n,x) = Au(n ,x) + \sum_{j=1}^k \beta_j u(n-\tau_j,x) +f(n,u(n,x)),\,\,\,  n \in \mathbb{Z}, x \in \Omega \subset \mathbb{R}^N, \beta_j\in\mathbb{R}\hspace{0.1cm}\mbox{and}\hspace{0.1cm} \tau_j \in \mathbb{Z},$$where $A$ is a closed linear operator defined on a Banach space $X$ and $\Delta^{\alpha}$ denotes the Gr\"unwald-Letnikov  fractional derivative of order $\alpha>0.$ If $X$ is a $UMD$ space, we provide this characterization only in terms of the $R$-boundedness of the operator-valued symbol associated to  the abstract model. To illustrate our results, we derive new qualitative properties of  nonlinear difference equations with shiftings, including  fractional versions of the logistic and Nagumo equations.
PB Elsevier
YR 2017
FD 2017
LK http://hdl.handle.net/10498/35469
UL http://hdl.handle.net/10498/35469
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026