Difference equations, as discrete analogues of differential equations, form a fundamental mathematical framework for describing systems that evolve incrementally over time or space. Coupled with ...

This rapidly evolving field extends classical discrete calculus by introducing non-integer, or fractional, orders of difference operators. Such an approach is particularly well suited to modelling ...

We survey many old and new results on solutions of the following pair of adjoint differential-difference equations: \begin{align*} \tag{1} up'(u) = - ap(u) - bp(u - 1 ...

In many biological and physical systems, feedback mechanisms depend on a set of thresholds associated with the state variables. Each feedback has a characteristic time scale. We suggest that ...