Sadek, LakhlifaAkgul, AliBataineh, Ahmad SamiHashim, Ishak2024-12-242024-12-2420242473-6988https://doi.org/10.3934/math.2024380https://hdl.handle.net/20.500.12604/8397This 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.eninfo:eu-repo/semantics/openAccesscotangent fractional derivativedelay cotangent fractional equationcotangent fractional Gronwall inequalitybound for the solutionuniqueness of solutionArticle9478197833N/AWOS:001171222200003Q12-s2.0-8518570125010.3934/math.2024380