Nonsymmetric and symmetric fractional calculi on arbitrary nonempty closed sets

作者：Benkhettou Nadia; Brito da Cruz Artur M C; Torres Delfim F M^*

来源：Mathematical Methods in the Applied Sciences, 2016, 39(2): 261-279.

DOI：10.1002/mma.3475

• discrete and continuous fractional calculi
• nonsymmetric and symmetric fractional calculi
• time scales

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.

• 出版日期2016-1