Nontrivial solutions for arbitrary order discrete relaxation equations with periodic boundary conditions

In this paper, we focus on two distinct types of nabla fractional relaxation equations with periodic boundary conditions. Our first step is to build the related Green’s functions and discover some of their characteristics. Next, using the appropriate fixed point theorems, we derive sufficient conditions for the existence of solutions to the problems under consideration. Further, to illustrate the applicability of our findings, we also offer two examples.