Existence and Stability of Positive Solutions for a Class of Delta Fractional Perturbed Problems

Abstract

The aim of the present work is to study a class of perturbed delta Riemann–Liouville (RL) fractional problems coupled with Dirichlet conditions. Our new results improve significantly upon the existing results, as we show that the related Green’s function, which can be expressed as an infinite series, is actually positive under suitable conditions. This allows us to prove several existence and nonexistence results using fixed point theory. Moreover, we deduce that the existing solution is Ulam–Hyers (UH) stable. In conclusion, we provide several examples demonstrating the relevance of our results.