In this study, we investigate the existence and multiplicity of solutions for a fractional discrete $p-$ Laplacian equation on $ \mathbb{Z} $, via the mountain pass lemma and Ekeland’s variational principle. Under suitable hypotheses on functions $V$ and $f$, we prove that this equation admits at least two nonnegative and nontrivial homoclinic solutions when the real parameter $\lambda >0$ is large enough.