Summary: Let \(\Omega\subset\mathbb{R}^N\) (\(N\geq 2\)) be a bounded domain with Lipschitz boundary. For each \(p\in(1,\infty)\) and \(s\in (0,1)\) we denote by \((-\Delta_p)^s\) the fractional \((s,p)\)-Laplacian operator. In this paper we study the existence of nontrivial solutions for a perturbation of the eigenvalue problem \((-\Delta_p)^s u=\lambda |u|^{p-2}u\), in \(\Omega\), \(u=0\), in \(\mathbb{R}^N\;\Omega\), with a fractional \((t,q)\)-Laplacian operator in the left-hand side of the equation, when \(t\in(0,1)\) and \(q\in(1,\infty)\) are such that \(s-N/p=t-N/q\). We show that nontrivial solutions for the perturbed eigenvalue problem exists if and only if parameter \(\lambda\) is strictly larger than the first eigenvalue of the \((s,p)\)-Laplacian.