Nonsymmetric and symmetric fractional calculi on arbitrary nonempty closed sets

摘要

We introduce a nabla, a delta, and a symmetric fractional calculus on arbitrary nonempty closed subsets of the real numbers. These fractional calculi provide a study of differentiation and integration of non-integer order on discrete, continuous, and hybrid settings. Main properties of the new fractional operators are investigated and some fundamental results presented, illustrating the interplay between discrete and continuous behaviors. Copyright (c) 2015John Wiley & Sons, Ltd.