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 ...

Difference equations, serving as the discrete analogue to differential equations, have long been a linchpin in the study of dynamic systems. These equations define sequences recursively, and their ...

SIAM Journal on Applied Mathematics, Vol. 19, No. 2 (Sep., 1970), pp. 334-339 (6 pages) An extension to difference equations of the now classical method of Krylov and Bogoljubov is presented. This ...

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 ...