Stability analysis of fractional differential system with Riemann-Liouville derivative
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TLDR
This paper focuses on establishing stability theorems for fractional differential system with Riemann-Liouville derivative, in particular the analysis covers the linear system, the perturbed system and the time-delayed system.About:
This article is published in Mathematical and Computer Modelling.The article was published on 2010-09-01 and is currently open access. It has received 190 citations till now. The article focuses on the topics: Generalizations of the derivative & Fractional calculus.read more
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A survey on the stability of fractional differential equations - Dedicated to Prof. Y.S. Chen on the Occasion of his 80th Birthday
TL;DR: A brief overview on the recent stability results of fractional differential equations and the analytical methods used are provided in this paper, where some conclusions for stability are similar to that of classical integer-order differential equations.
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On Riemann-Liouville and Caputo Derivatives
TL;DR: In this article, the important properties of the Riemann-Liouville (RL) derivative, one of the most commonly used fractional derivatives, are discussed, and the partial fractional derivative is also introduced.
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Fractional dynamical system and its linearization theorem
Changpin Li,Yutian Ma +1 more
TL;DR: In this paper, the authors established the similar relationship between a fractional differential equation and the corresponding fractional flow under a reasonable condition and proved Audounet-Matignon-Montseny conjecture.
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Stability and Stabilization of Fractional-Order Linear Systems Subject to Input Saturation
TL;DR: Gronwall-Bellman lemma and sector bounded condition of the saturation function are exploited and a bilinear matrix inequality for stability test and an algorithm for estimation of the stable region are provided.
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A mathematical model of dengue transmission with memory
TL;DR: It is shown that even though R 0 is less than unity, the DFE may not be always stable, and the system exhibits a Hopf-type bifurcation, and making R 0 1 for controlling the disease is no longer a sufficient condition.
References
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Book
Perturbation theory for linear operators
TL;DR: The monograph by T Kato as discussed by the authors is an excellent reference work in the theory of linear operators in Banach and Hilbert spaces and is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory.
Book
Theory and Applications of Fractional Differential Equations
TL;DR: In this article, the authors present a method for solving Fractional Differential Equations (DFE) using Integral Transform Methods for Explicit Solutions to FractionAL Differentially Equations.
Book
One-Parameter Semigroups for Linear Evolution Equations
Klaus-Jochen Engel,Rainer Nagel +1 more
TL;DR: In this paper, Spectral Theory for Semigroups and Generators is used to describe the exponential function of a semigroup and its relation to generators and resolvents.