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.