@article{Hyder2024, 
author = {Abd-Allah Hyder and Hüseyin Budak and Mohamed A. Barakat},
title = {Milne-Type inequalities via expanded fractional operators: A comparative study with different types of functions},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {5},
pages = {11228-11246},
keywords = {fractional integrals, Milne-type inequalities, functions of bounded variation, convex functions, bounded functions},
url = {https://www.sciopen.com/article/10.3934/math.2024551},
doi = {10.3934/math.2024551},
abstract = {This study focused on deriving Milne-type inequalities using expanded fractional integral operators. We began by establishing a key equality associated with these operators. Using this equality, we explored Milne-type inequalities for functions with convex derivatives, supported by an illustrative example for clarity. Additionally, we investigated Milne-type inequalities for bounded and Lipschitzian functions utilizing fractional expanded integrals. Finally, we extended our exploration to Milne-type inequalities involving functions of bounded variation.}
}