@article{Aly2024, 
author = {Elkhateeb S. Aly and Y. A. Madani and F. Gassem and A. I. Saied and H. M. Rezk and Wael W. Mohammed},
title = {Some dynamic Hardy-type inequalities with negative parameters on time scales nabla calculus},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {2},
pages = {5147-5170},
keywords = {Hardy-type inequalities with negative parameters, time scales, reverse Hölder's inequality, chain rule},
url = {https://www.sciopen.com/article/10.3934/math.2024250},
doi = {10.3934/math.2024250},
abstract = {In this paper, we establish some new dynamic Hardy-type inequalities with negative parameters on time scales nabla calculus by applying the reverse H ölder's inequality, integration by parts,  and chain rule on time scales nabla calculus. As special cases of our results (when        T    =    R  ),  we get the continuous analouges of inequalities proven by Benaissa and Sarikaya, and when              T      =      N              0      , the results to the best of the authors' knowledge are essentially new.}
}