Gronwall inequality and existence of solutions for differential equations with generalized Hattaf fractional derivative
Volume 27, Issue 1, pp 18--27
http://dx.doi.org/10.22436/jmcs.027.01.02
Publication Date: February 10, 2022
Submission Date: November 24, 2021
Revision Date: December 28, 2021
Accteptance Date: January 07, 2022
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Authors
Kh. Hattaf
- Equipe de Recherche en Modelisation et Enseignement des Mathematiques (ERMEM), Centre Regional des Metiers de l'Education et de la Formation (CRMEF), 20340 Derb Ghalef, Casablanca, Morocco.
- Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben Msik, Hassan II University of Casablanca, P.O. Box 7955, Sidi Othman, Casablanca, Morocco.
A. A. Mohsen
- Department of Mathematics, College of Education for Pure Science (Ibn Al-Haitham) , University of Baghdad, Iraq.
- Ministry of Education, Rusafa 1, Baghdad, Iraq.
H. F. Al-Husseiny
- Department of Mathematics, College of Education for Pure Science (Ibn Al-Haitham), University of Baghdad, Iraq.
Abstract
The classical Gronwall inequality is one of the basic tools in the theory of differential and integral equations.
In this paper, a new version of this inequality is presented and extended to differential equations with the generalized Hattaf
fractional derivative involving non-singular kernel. The existence and uniqueness of solutions for such last type of
fractional differential equations are rigorously investigated. Furthermore, an application is presented to
study the Ulam-Hyers stability of certain equations.
Share and Cite
ISRP Style
Kh. Hattaf, A. A. Mohsen, H. F. Al-Husseiny, Gronwall inequality and existence of solutions for differential equations with generalized Hattaf fractional derivative, Journal of Mathematics and Computer Science, 27 (2022), no. 1, 18--27
AMA Style
Hattaf Kh., Mohsen A. A., Al-Husseiny H. F., Gronwall inequality and existence of solutions for differential equations with generalized Hattaf fractional derivative. J Math Comput SCI-JM. (2022); 27(1):18--27
Chicago/Turabian Style
Hattaf, Kh., Mohsen, A. A., Al-Husseiny, H. F.. "Gronwall inequality and existence of solutions for differential equations with generalized Hattaf fractional derivative." Journal of Mathematics and Computer Science, 27, no. 1 (2022): 18--27
Keywords
- Gronwall inequality
- Hattaf fractional derivative
- fractional differential equation
- Ulam-Hyers stability
MSC
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