English

The q-fractional analogue for Gronwall-type inequality

Dynamical Systems 2016-09-20 v1 Classical Analysis and ODEs

Abstract

In this article, we utilize \emph{q}--fractional Caputo initial value problems of order 0<α10<\alpha\leq 1 to derive a \emph{q}--analogue for Gronwall--type inequality. Some particular cases are derived where \emph{q}--Mittag--Leffler functions and \emph{q}--exponential type functions are used. An example is given to illustrate the validity of the derived inequality.

Keywords

Cite

@article{arxiv.1305.2082,
  title  = {The q-fractional analogue for Gronwall-type inequality},
  author = {Thabet Abdeljawad and Jehad Alzabut},
  journal= {arXiv preprint arXiv:1305.2082},
  year   = {2016}
}