English

Chain rules and inequalities for the BHT fractional calculus on arbitrary time scales

Classical Analysis and ODEs 2017-03-03 v1

Abstract

We develop the Benkhettou-Hassani-Torres fractional (noninteger order) calculus on time scales by proving two chain rules for the α\alpha-fractional derivative and five inequalities for the α\alpha-fractional integral. The results coincide with well-known classical results when the operators are of (integer) order α=1\alpha = 1 and the time scale coincides with the set of real numbers.

Keywords

Cite

@article{arxiv.1611.09049,
  title  = {Chain rules and inequalities for the BHT fractional calculus on arbitrary time scales},
  author = {Eze R. Nwaeze and Delfim F. M. Torres},
  journal= {arXiv preprint arXiv:1611.09049},
  year   = {2017}
}

Comments

This is a preprint of a paper whose final and definite form is published in 'Arabian Journal of Mathematics', ISSN 2193-5343 (Print) 2193-5351 (Online). Paper submitted 25/Feb/2016; revised 24/Sept/2016; accepted 28/Nov/2016