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 ...

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 ...

This paper considers the estimation of the parameters of general systems of stochastic differential-difference equations in which the lag parameters themselves are treated as unknown and are not ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...

In this paper we investigate the effectiveness of alternating direction implicit (ADI) time-discretization schemes in the numerical solution of the three-dimensional Heston-Hull-White partial ...

If today's college students could find a way to get their hands on a copy of Facebook's latest neural network, they could cheat all the way through Calc 3. They could even solve the differential ...