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Fractional derivatives and cauchy problem for differential equations of fractional order
, 2020Editorial Note: This is a paper by M.M. Djrbashian and A.B. Nersesian of 1968, that was published in Russian. There is a constant interest to Djrbashian’s contributions to the topic of fractional calculus and theory of Mittag-Leffler function ...
M.M. Dzherbashian, A. B. Nersesian
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Fractional-Order Models of the Ultracapacitors
2013In the paper, dynamic behavior of the ultracapacitors is investigated and analyzed. The ultracapacitors are represented by equivalent electrical circuit models and mathematically described by fractional-order differential equations. The identification procedure is proposed to identify the parameters of the models.
Pawel Skruch, Wojciech Mitkowski
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Bifurcation Mechanism for Fractional-Order Three-Triangle Multi-delayed Neural Networks
Neural Processing Letters, 2022Changjin Xu +4 more
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Intermittent control for finite-time synchronization of fractional-order complex networks
Neural Networks, 2021Lingzhong Zhang, Jie Zhong, Jianquan Lu
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Fractional order describing functions
Signal Processing, 2015This paper addresses limit cycles and signal propagation in dynamical systems with backlash. The study follows the describing function (DF) method for approximate analysis of nonlinearities and generalizes it in the perspective of the fractional calculus.
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Bifurcation Properties for Fractional Order Delayed BAM Neural Networks
Cognitive Computation, 2021Changjin Xu +4 more
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Fractional-order observers design for fractional-order systems with unknown inputs
2012This paper considers a method to design the functional observers for continuous-time linear fractional-order systems with unknown inputs. The conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of observers with the fractional-order satisfying ...
N'Doye, Ibrahima +2 more
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Fractional-Order PID Controller and Fractional-Order Disturbance Observer
2018Over the past decades, some important results on fractional-order controllers have been proposed for various systems. Podlubny introduced the concept of a fractional-order PIλDμ controller, including a fractional-order integrator and a fractional-order differentiator. A well-known fractional-order controller was presented by Oustaloup et al.
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On Differences of Fractional Order
Proceedings of the London Mathematical Society, 1957openaire +2 more sources