Journal ArticleDOI
Lyapunov functions for fractional order systems
TLDR
A new lemma for the Caputo fractional derivatives, when 0 α 1 , is proposed, which has proved to be useful in order to apply the fractional-order extension of Lyapunov direct method, to demonstrate the stability of many fractional order systems, which can be nonlinear and time varying.About:
This article is published in Communications in Nonlinear Science and Numerical Simulation.The article was published on 2014-09-01. It has received 1010 citations till now. The article focuses on the topics: Fractional calculus & Lyapunov function.read more
Citations
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Journal ArticleDOI
Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems
TL;DR: The paper presents two new lemmas related to the Caputo fractional derivatives and a theorem for proving uniform stability in the sense of Lyapunov for fractional order systems and is applied to the stability analysis of two Fractional Order Model Reference Adaptive Control schemes.
Journal ArticleDOI
Adaptive Fuzzy Backstepping Control of Fractional-Order Nonlinear Systems
TL;DR: An adaptive fuzzy backstepping control method for a class of uncertain fractional-order nonlinear systems with unknown external disturbances that ensures convergence of the tracking error is constructed.
Journal ArticleDOI
Volterra-type Lyapunov functions for fractional-order epidemic systems
TL;DR: In this article, the authors prove an elementary lemma which estimates fractional derivatives of Volterra-type Lyapunov functions in the sense Caputo when α ∈ ( 0, 1 ).
Journal ArticleDOI
Modeling and analysis of COVID-19 epidemics with treatment in fractional derivatives using real data from Pakistan
TL;DR: A fractional-order epidemic model with two different operators called the classical Caputo operator and the Atangana–Baleanu–Caputo operator for the transmission of COVID-19 epidemic is proposed and analyzed and the treatment compartment is included in the population which determines the impact of alternative drugs applied for treating the infected individuals.
Journal ArticleDOI
Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations
TL;DR: In this article, a semi-analytical method based on Adomian polynomials and a fractional Taylor series was proposed to investigate chaotic behavior and stability of fractional differential equations within a new generalized Caputo derivative.
References
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Book
Applied Nonlinear Control
TL;DR: Covers in a progressive fashion a number of analysis tools and design techniques directly applicable to nonlinear control problems in high performance systems (in aerospace, robotics and automotive areas).
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.
Journal ArticleDOI
Analysis of Fractional Differential Equations
Kai Diethelm,Neville J. Ford +1 more
TL;DR: In this paper, the authors discuss existence, uniqueness, and structural stability of solutions of nonlinear differential equations of fractional order, and investigate the dependence of the solution on the order of the differential equation and on the initial condition.
Book
Stable Adaptive Systems
TL;DR: Stability theory simple adaptive systems adaptive observers the control problem persistent excitation error models robust adaptive controlThe control problem - relaxation of assumptions multivariable adaptive systems applications of adaptive control.