Fractional Discrete Systems with Sequential h-differences

In the paper we study the subject of positivity of systems with sequential fractional difference. We give formulas for the unique solutions of systems in linear and semi-linear cases. The positivity of systems is considered

Nonsymmetric and Symmetric Fractional Calculi on Arbitrary Nonempty Closed Sets

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 noninteger 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.Comment: This is a preprint of a paper whose final and definite form will be published in Mathematical Methods in the Applied Sciences, ISSN 0170-4214. Submitted 05/March/2014; revised 24/Feb/2015; accepted 25/Feb/2015. arXiv admin note: text overlap with arXiv:1405.281