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Fractional signals and systems [PDF]
Signal Processing, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Manuel Duarte Ortigueira +3 more
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From Wavelet Analysis to Fractional Calculus: A Review
Mathematics, 2023 In this note, we review some important results on wavelets, together with their main applications. Similarly, we present the main results on fractional calculus and their current applications in pure and applied science. We conclude the paper showing the
Emanuel Guariglia +2 more
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Sensors, 2022 In recent times, many different types of systems have been based on fractional derivatives. Thanks to this type of derivatives, it is possible to model certain phenomena in a more precise and desirable way.
Rafał Brociek +4 more
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Fractal and Fractional, 2023 This study deals with the controllability of multi-term fractional-order stochastic systems with impulsive effects and state-dependent delay that exhibit damping behavior.
G. Arthi, M. Vaanmathi, Yong-Ki Ma
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International Journal of Applied Mathematics and Computer Science, 2021 The divisibility of the second-order minors of the numerators of transfer matrices by their minimal denominators for cyclic fractional linear systems is analyzed. It is shown that all nonzero second-order minors of the numerators of the transfer matrices
Kaczorek Tadeusz
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Sampled-Data Stabilization of Fractional Linear System under Arbitrary Sampling Periods
Fractal and Fractional, 2022 The sampled-data stabilization of a fractional continuous linear system under arbitrary sampling periods was first investigated in this paper wherein novel co-designed sampled-data controllers were constructed based on the compensation of scaling gains ...
Kecai Cao +3 more
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On Fractional Benney Type Systems
SIAM Journal on Mathematical Analysis, 2023 This paper introduces fractional type evolutionary equations modeling the interaction between short waves and long waves. We consider a fractional Benney type system, which is given by a fractional Schrödinger equation coupled with a fractional porous medium equation. Under the assumption of weak coupling or small initial data related to the fractional
Wladimir Neves, Dionicio Orlando
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Fractal and Fractional, 2023 This paper concerns a nonhomogeneous singular fractional order system, with two frictional damping terms. This system can be considered as a generalization of the so-called Timoshenko system.
Said Mesloub, Reem K. Alhefthi
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Fractional free space, fractional lenses, and fractional imaging systems [PDF]
Journal of the Optical Society of America A, 2003 Continuum extensions of common dual pairs of operators are presented and consolidated, based on the fractional Fourier transform. In particular, the fractional chirp multiplication, fractional chirp convolution, and fractional scaling operators are defined and expressed in terms of their common nonfractional special cases, revealing precisely how they ...
Sümbül, U., Ozaktas, H., M.
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Fractional-hyperbolic systems [PDF]
Fractional Calculus and Applied Analysis, 2013 We describe a class of evolution systems of linear partial differential equations with the Caputo-Dzhrbashyan fractional derivative of order $α\in (0,1)$ in the time variable $t$ and the first order derivatives in spatial variables $x=(x_1,...,x_n)$, which can be considered as a fractional analogue of the class of hyperbolic systems.
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