Incomplete Riemann-Liouville fractional derivative operators and incomplete hypergeometric functions
Classical Analysis and ODEs
2019-01-16 v1
Abstract
In this paper, the incomplete Pochhammer ratios are defined in terms of the incomplete beta function . With the help of these incomplete Pochhammer ratios, we introduce new incomplete Gauss, confluent hypergeometric and Appell's functions and investigate several properties of them such as integral representations, derivative formulas, transformation formulas, and recurrence relation. Furthermore, an incomplete Riemann-Liouville fractional derivative operators are introduced. This definition helps us to obtain linear and bilinear generating relations for the new incomplete Gauss hypergeometric functions.
Keywords
Cite
@article{arxiv.1901.04825,
title = {Incomplete Riemann-Liouville fractional derivative operators and incomplete hypergeometric functions},
author = {Mehmet Ali Özarslan and Ceren Ustaoğlu},
journal= {arXiv preprint arXiv:1901.04825},
year = {2019}
}