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

Discrete fractional calculus (DFC) is a contemporary branch of fractional calculus with a discrete form. DFC is continuously spreading in neural networks, chaotic maps, engineering practice, and image encryption, which is appropriately assumed for discrete-time modeling in continuum problems. In this study, we solve a few problems with classic and fractional difference operators using a discrete variant of the Adomian decomposition method (ADM). This method helps to find the solutions of linear and nonlinear classic and fractional difference problems (CDPs and FDPs). A few examples are given to clarify and confirm the obtained results and some of particular cases of CDPs and FDPs are highlighted.