Impulsive fractional order integrodifferential equation via fractional operators.
PLoS ONE, 2023 In this paper, we establish the existence and uniqueness of the solution to fractional equations abstract integrodifferential equation with impulsive as [Formula: see text] where [Formula: see text] and we used the fixed point theorems due to Banach ...
Ahmad Al-Omari, Hanan Al-Saadi
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A fractional spline collocation method for the fractional order logistic equation [PDF]
, 2017 We construct a collocation method based on the fractional B-splines to solve a nonlinear differential problem that involves fractional derivative, i.e. the fractional order logistic equation.
Pezza, L., Pitolli, F.
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Mixed Order Fractional Observers for Minimal Realizations of Linear Time-Invariant Systems
Algorithms, 2018 Adaptive and non-adaptive minimal realization (MR) fractional order observers (FOO) for linear time-invariant systems (LTIS) of a possibly different derivation order (mixed order observers, MOO) are studied in this paper.
Manuel A. Duarte-Mermoud +3 more
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On Passivity of Fractional Order Systems [PDF]
SIAM Journal on Control and Optimization, 2019 We generalize notions of passivity and dissipativity to fractional order systems. Similar to integer order systems, we show that the proposed definitions generate analogous stability and compositionality properties for fractional order systems as well.
Mohsen Rakhshan +2 more
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On fraction order modeling and control of dynamical systems [PDF]
, 2009 This paper demonstrates the feasibility of modeling any dynamical system using a set of fractional order di®erential equations, including distributed and lumped systems.
Kahalil, Islam +3 more
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Fractional Newton-Raphson Method Accelerated with Aitken's Method
, 2021 In the following document, we present a way to obtain the order of convergence of the Fractional Newton-Raphson (F N-R) method, which seems to have an order of convergence at least linearly for the case in which the order $\alpha$ of the derivative is ...
Brambila-Paz, F. +3 more
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Fractional order modelling of fractional-order holds [PDF]
Nonlinear Dynamics, 2012 Discrete time control systems require sample-and-hold circuits to perform the conversion from digital to analog. Fractional-Order Holds (FROHs) are an interpolation between the classical zero and first order holds and can be tuned to produce better system performance.
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Conformable Fractional Order Sliding Mode Control for a Class of Fractional Order Chaotic Systems [PDF]
International Journal of Industrial Electronics, Control and Optimization, 2019 In this paper, a novel conformable fractional order (FO) sliding mode control technique is studied for a class of FO chaotic systems in the presence of uncertainties and disturbances.
Sara Haghighatnia +2 more
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Fractional-Order Traveling Wave Approximations for a Fractional-Order Neural Field Model
Frontiers in Computational Neuroscience, 2022 In this work, we establish a fractional-order neural field mathematical model with Caputo's fractional derivative temporal order α considering 0 < α < 2, to analyze the effect of fractional-order on cortical wave features observed preceding seizure
Laura R. González-Ramírez
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Fractional-Order LQR and State Observer for a Fractional-Order Vibratory System
Applied Sciences, 2021 The present study uses linear quadratic regulator (LQR) theory to control a vibratory system modeled by a fractional-order differential equation. First, as an example of such a vibratory system, a viscoelastically damped structure is selected.
Akihiro Takeshita +3 more
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