Existence of Positive Solutions for a Class of Nabla Fractional Boundary Value Problems
Nikolay D. Dimitrov, Jagan Mohan Jonnalagadda
Abstract
In this manuscript, we study a class of equations with two different Riemann–Liouville-type orders of nabla difference operators. We show some new and fundamental properties of the related Green’s function. Depending on the values of the orders of the operators, we split our research into two main cases, and for each one of them, we obtain suitable conditions under which we prove that the considered problem possesses a positive solution. We consider the latter to be the main novelty in this work. Our main tool in both cases of our study is Guo–Krasnoselskii’s fixed point theorem. In the end, we give particular examples in order to offer a concrete demonstration of our new theoretical findings, as well as some possible future work in this direction.