Existence Results for Singular Nabla Fractional Perturbed Problems

The aim of the present work is to study a class of singular perturbed nabla fractional problems coupled with Dirichlet conditions. Under sufficient conditions we show that the related Green’s function that can be expressed as an infinite series, is positive, which improves significantly the previous results for perturbed fractional problems in general. This allows us to prove an existence result using mixed monotone approach. In conclusion, we provide an example demonstrating the relevance of our results.