We study a discrete boundary value problem involving the Riemann-Liouville fractional operator. In particular, we introduce a discrete fractional summing boundary value problem that parallels the integral boundary value problem for fractional differential equations. By generalizing a commonly used fractional difference operator, we derive the corresponding Green's function and reformulate the problem as a fixed-point equation. The existence and multiplicity of positive solutions are established. Two illustrative examples are provided to demonstrate the applicability of the theoretical results, and numerical simulations are included for further validation.
Kang et al. (Thu,) studied this question.