]>
2019
12
9
ISSN 2008-1898
0
Stability analysis of the generalized fractional differential equations with and without exogenous inputs
Stability analysis of the generalized fractional differential equations with and without exogenous inputs
en
en
The stability conditions of the fractional differential equations described by the Caputo generalized fractional derivative have been addressed. The generalized asymptotic stability of a class of the fractional differential equations has been investigated. The fractional input stability in the context of the fractional differential equations described by the Caputo generalized fractional derivative has been introduced. The Lyapunov characterizations of the generalized asymptotic stability and the generalized fractional input stability of the fractional differential equations with or without inputs have been provided. Several examples illustrating the main results of the paper have been proposed. The Caputo generalized fractional derivative and the generalized Gronwall lemma have been used.
562
572
Ndolane
Sene
Laboratoire Lmdan, Departement de Mathematiques de la Decision
Universite Cheikh Anta Diop de Dakar
Senegal
ndolanesene@yahoo.fr
Caputo generalized fractional derivative
asymptotic stability
fractional differential equations
Article.1.pdf
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Continuous dependence solutions for Hilfer fractional differential equations with nonlocal conditions
Continuous dependence solutions for Hilfer fractional differential equations with nonlocal conditions
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en
We discuss the existence, uniqueness and continuous dependence of solution for a non-autonomous semilinear Hilfer fractional differential equation with nonlocal conditions in the space of weighted continuous functions. By means of the Krasnoselskii's fixed point theorem and the generalized Gronwall's inequality, we establish the desired results.
573
581
Mohamed I.
Abbas
Department of Mathematics and Computer Science, Faculty of Science
Alexandria University
Egypt
miabbas77@gmail.com
Hilfer fractional derivative
Krasnoselskii's fixed point theorem
Gronwall's inequality
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]