On Dynamic Systems in the Frame of Singular Function Dependent Kernel Fractional Derivatives

Thabet Abdeljawad, Fadila Madjidi, Fahd Jarad and Ndolane Sene
Additional contact information
Thabet Abdeljawad: Department of Mathematics and General Sciences, Prince Sultan University, P. O. Box 66833, Riyadh 11586, Saudi Arabia
Fadila Madjidi: Department of Mathematics, University of Mohamed Boudiaf-PB 166, M’sila 28000, Algeria
Fahd Jarad: Department of Mathematics, Çankaya University, 06790 Etimesgut, Ankara, Turkey
Ndolane Sene: Laboratoire Lmdan, Dèpartement de Mathèmatiques de la Dècision, Universitè Cheikh Anta Diop de Dakar, Facultè des Sciences Economiques et Gestion, Dakar Fann BP 5683, Senegal

Mathematics, 2019, vol. 7, issue 10, 1-13

Abstract: In this article, we discuss the existence and uniqueness theorem for differential equations in the frame of Caputo fractional derivatives with a singular function dependent kernel. We discuss the Mittag-Leffler bounds of these solutions. Using successive approximation, we find a formula for the solution of a special case. Then, using a modified Laplace transform and the Lyapunov direct method, we prove the Mittag-Leffler stability of the considered system.

Keywords: generalized fractional operators; Mittag-Leffler bound; Mittag-Leffler stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/10/946/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/10/946/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:10:p:946-:d:275532

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().