@article{Sadek2024, 
author = {Lakhlifa Sadek and Ali Akgül and Ahmad Sami Bataineh and Ishak Hashim},
title = {A cotangent fractional Gronwall inequality with applications},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {4},
pages = {7819-7833},
keywords = {cotangent fractional derivative, delay cotangent fractional equation, cotangent fractional Gronwall inequality, bound for the solution, uniqueness of solution},
url = {https://www.sciopen.com/article/10.3934/math.2024380},
doi = {10.3934/math.2024380},
abstract = {This article presents the cotangent fractional Gronwall inequality, a novel understanding of the Gronwall inequality within the context of the cotangent fractional derivative. We furnish an explanation of the cotangent fractional derivative and emphasize a selection of its distinct characteristics before delving into the primary findings. We present the cotangent fractional Gronwall inequality (Lemma 3.1) and a Corollary 3.2 using the Mittag-Leffler function, we establish singularity and compute an upper limit employing the Mittag-Leffler function for solutions in a nonlinear delayed cotangent fractional system, illustrating its practical utility. To underscore the real-world relevance of the theory, a tangible instance is given.}
}