Existence theory for nabla fractional three-point boundary value problems via continuation methods for contractive maps - Jonnalagadda, Jagan Mohan (Topological Methods in Nonlinear Analysis, 2023)
In this article, we analyse an $α$-th order, $1 < α ≤ 2$, nabla fractional three-point boundary value problem (BVP). We construct the Green's function associated to this problem and derive a few of its important properties.We then establish sufficient conditions on existence and uniqueness of solutionsfor the corresponding nonlinear BVP using the modern ideas of continuation methods for contractive maps. Our results extend recent results on nabla fractional BVPs. Finally, we provide an example to illustrate the applicability of main results.