%0 Journal Article 
%A Girona, I.
%A Murillo Arcila, Marina
%T Maximal ℓp-regularity of multi-term fractional equations with delay.
%D 2021
%@ 1099-1476

%U http://hdl.handle.net/10498/35360
%X We provide a characterization for the existence and uniqueness of solutions in the space of vector-valued sequences $\ell_p(\mathbb{Z},X)$ for the multi-term fractional delayed model in the form:
$$
\Delta^\alpha u(n)+\lambda \Delta^\beta u(n)=Au(n)+u(n-\tau)+f(n),~n\in\mathbb{Z},\alpha, \beta\in\mathbb{R}_{+},\tau\in\mathbb{Z},~\lambda\in\mathbb{R}
$$
where X is a Banach space, A is a closed linear operator with domain D(A) defined on X, $f\in \ell_p(\mathbb{Z},X)$ and  $\Delta^{\gamma}$ denotes the Gr\"unwald-Letkinov fractional derivative of order $\gamma>0$. We also give some conditions to ensure the  existence of solutions when adding nonlinearities. Finally, we illustrate our results with an example given by a general abstract nonlinear model that includes  the fractional Fisher equation with delay.
%~ Universidad de Cádiz