Positive Solutions for Nabla Fractional Three-Point Boundary Value Problems

The aim of the present work is to study a class of nabla fractional problems with two different nabla Riemann–Liouville operators and three-point parameter-dependent boundary conditions. First, we derive the expression of the Green’s function; then, we deduce a few useful inequalities with it, and we establish an interval for the parameter in which the Green’s function is always positive. Using these properties, we manage to prove some non-existence, existence and multiplicity results using different fixed-point theorems. At the end, we give a few examples that verify and clarify the applications of our results.