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

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Department of Mathematics and General Sciences, Prince Sultan University, P. O. Box 66833, Riyadh 11586, Saudi Arabia
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Department of Medical Research, China Medical University, Taichung 40402, Taiwan
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Department of Mathematics, University of Mohamed Boudiaf-PB 166, M’sila 28000, Algeria
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Department of Mathematics, Çankaya University, 06790 Etimesgut, Ankara, Turkey
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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
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Authors to whom correspondence should be addressed.
Mathematics 2019, 7(10), 946; https://doi.org/10.3390/math7100946
Received: 15 August 2019 / Revised: 17 September 2019 / Accepted: 9 October 2019 / Published: 11 October 2019
(This article belongs to the Special Issue Stability Analysis of Fractional Systems)
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. View Full-Text
Keywords: generalized fractional operators; Mittag-Leffler bound; Mittag-Leffler stability generalized fractional operators; Mittag-Leffler bound; Mittag-Leffler stability
MDPI and ACS Style

Abdeljawad, T.; Madjidi, F.; Jarad, F.; Sene, N. On Dynamic Systems in the Frame of Singular Function Dependent Kernel Fractional Derivatives. Mathematics 2019, 7, 946.

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