This article aims to use Bohnenblust–Karlin’s fixed point theorem to obtain new results for the impulsive inclusions with infinite delay in Banach space given by the form
\[
(P)\;
\begin{cases}
{}^{c}D_{t}^{\alpha}x(t) – A x(t) \in F(t, x_t), & t \in J = [0, b],\; t \ne t_i,\\[6pt]
x(t) = \Psi(t), & t \in (-\infty, 0],\\[6pt]
\Delta x(t_i) = I_i(x(t_i^-)), & i = 1, \ldots, m,
\end{cases}
\]
where ${}^{c}D^{\alpha}$ is the Caputo derivative. We examine the case when the multivalued function $F$ is a Carathéodory function and the linear part is a sectorial operator defined on Banach space. Also, we provide an example to elaborate the outcomes.