On Hilfer fractional difference operator
General Mathematics
2020-03-17 v3
Abstract
In this article, a new definition of fractional Hilfer difference operator is introduced. Definition based properties are developed and utilized to construct fixed point operator for fractional order Hilfer difference equations with initial condition. We acquire some conditions for existence, uniqueness, Ulam-Hyers and Ulam-Hyers-Rassias stability. Modified Gronwall's inequality is presented for discrete calculus with the delta difference operator.
Cite
@article{arxiv.1911.06986,
title = {On Hilfer fractional difference operator},
author = {Syed Sabyel Haider and Mujeeb ur Rehman and Thabet Abdeljawad},
journal= {arXiv preprint arXiv:1911.06986},
year = {2020}
}
Comments
26 pages, 2 figures, change in starting point of domain of definition