A cotangent fractional Gronwall inequality with applications

Lakhlifa Sadek; Ali Akgül; Ahmad Sami Bataineh; Ishak Hashim; Lakhlifa Sadek; Ali Akgül; Ahmad Sami Bataineh; Ishak Hashim

doi:10.3934/math.2024380

AIMS Mathematics

2024, Volume 9, Issue 4: 7819-7833. doi: 10.3934/math.2024380

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A cotangent fractional Gronwall inequality with applications

1.
Department of Mathematics, Faculty of Sciences and Technology, BP 34. Ajdir 32003 Al-Hoceima, Abdelmalek Essaadi University, Tetouan, Morocco
2.
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
3.
Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulevard, PC: 99138, Nicosia /Mersin 10, Turkey
4.
Siirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt, Turkey
5.
Department of Mathematics, Faculty of Science, Al-Balqa Applied University, 19117 Al Salt, Jordan
6.
Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia (UKM), Bangi 43650, Selangor, Malaysia
7.
Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman P.O. Box 346, United Arab Emirates

Received: 27 December 2023 Revised: 31 January 2024 Accepted: 06 February 2024 Published: 23 February 2024
MSC : 34A08, 34K37

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.
Citation: Lakhlifa Sadek, Ali Akgül, Ahmad Sami Bataineh, Ishak Hashim. A cotangent fractional Gronwall inequality with applications[J]. AIMS Mathematics, 2024, 9(4): 7819-7833. doi: 10.3934/math.2024380

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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.

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