Discrete ADM: A tools for solving a class of classic and fractional difference problems

Discrete fractional calculus (DFC) is continuously spreading in the neural networks, chaotic maps, engineering practice, and image encryption, which is appropriately assumed for discrete-time modelling in continuum problems. For solving problems including difference operators (classic and fractional), we employ a discrete version of the Adomian decomposition method (ADM). This method help to find the solutions of linear and nonlinear classic and fractional difference problems (CDPs and FDPs). Examples are given to clarify and confirm the obtained results and some of particular cases of CDPs and FDPs are highlighted.