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.

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Keywords

• Gronwall inequality
• Hattaf fractional derivative
• fractional differential equation
• Ulam-Hyers stability

MSC

•  26A33
•  26D15
•  34D10
•  34D20

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