English

Chain rule formula and generalized mean value theorem for nabla fractional differentiation on time scale

Classical Analysis and ODEs 2025-01-16 v1

Abstract

The nabla fractional derivative, which was introduced by Gogoi et.al., generalized the ordinary derivative with non-integer order, and unifies the continuous and discrete analysis using backward operator. In this study, we proposed a modification of their definition. The main focus of this work is to introduce a chain rule formula and a generalized mean value theorem for nabla fractional differentiation on time scale. Results of this study will be applied in finding the sum of a finite series.

Keywords

Cite

@article{arxiv.2501.08596,
  title  = {Chain rule formula and generalized mean value theorem for nabla fractional differentiation on time scale},
  author = {Gaddiel L. Dorado and Mark Allien D. Roble},
  journal= {arXiv preprint arXiv:2501.08596},
  year   = {2025}
}