We consider a boundary value problem involving a fractional differential equation with a g-Caputo fractional derivative. This paper establishes some new criteria for the existence of solutions to the problem, differing from those obtained by previous researchers. The method is based on the construction of a novel Green’s function and the application of the Schauder fixed point theorem. Examples are provided to illustrate the fundamental distinctions between our results and earlier work.

In this paper, we first introduce a new class of bilevel weak vector variational inequality problems in locally convex Hausdorff topological vector spaces. Then, using the Kakutani-Fan-Glicksberg fixed-point theorem, we establish some existence conditions of the solution for this problem.