On semipositone discrete fractional boundary value problems with non-local boundary conditions

Abstract

We consider the existence of at least one positive solution to the discrete fractional equation , where and , equipped with a two-point boundary condition that can possibly be both non-local and nonlinear. Due to the fact that f is allowed to be negative for some values of t and y, we consider here the semipositone problem. In addition to discussing conditions under which this problem is guaranteed to have at least one positive solution for small values of , we provide an example to illustrate the use of our results. Due to the generality of our results, we include many boundary conditions as special cases such as the conjugate- and multipoint-type conditions.