A cotangent fractional Gronwall inequality with applications-Reference-Cited by-同舟云学术

A cotangent fractional Gronwall inequality with applications

Published:2024 Issue:4 Volume:9 Page:7819-7833
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Sadek Lakhlifa¹,Akgül Ali²³⁴,Bataineh Ahmad Sami⁵,Hashim Ishak⁶⁷

Affiliation:

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

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Reference32 articles.

1. M. Caputo, M. Fabrizio, A new definition of fractional derivative without singular kernel, Progr. Fract. Differ. Appl., 1 (2015), 73–85.

2. J. Losada, J. J. Nieto, Properties of a new fractional derivative without singular kernel, Progr. Fract. Differ. Appl., 1 (2015), 87–92.

3. A. Atangana, D. Baleanu, New fractional derivatives with non-local and non-singular kernels: Theory and application to heat transfer model, Therm. Sci., 20 (2016), 763–769.

4. F. Jarad, T. Abdeljawad, J. Alzabut, Generalized fractional derivatives generated by a class of local proportional derivatives, Eur. Phys. J. Spec. Top., 226 (2017), 3457–3471. https://doi.org/10.1140/epjst/e2018-00021-7

5. A. N. Kochubei, General fractional calculus, evolution equations, and renewal processes, Integr. Equ. Oper. Theory, 71 (2011), 583–600. https://doi.org/10.1007/s00020-011-1918-8

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