Solvability of Nonlinear Discrete Fractional Equations with Mixed-Order Nabla Operators and Dirichlet Boundaries

Abstract

In this manuscript, we study the solvability of a class of mixed-order nabla fractional equations coupled with Dirichlet conditions. Based on the obtained Green’s function and its properties, we establish existence, nonexistence, and multiplicity results using fixed point theory. In the end, we give some numerical examples that verify our theoretical results.