scholarly journals $$L^p$$ properties of non-Archimedean fractional differentiation operators

2021 ◽  
Vol 12 (4) ◽  
Author(s):  
Anatoly N. Kochubei
Keyword(s):  
Fractional Differentiation

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

MIXED FRACTIONAL DIFFERENTIATION OPERATORS IN HÖLDER SPACES DEFINED BY USUAL HÖLDER CONDITION

2019 ◽  
Author(s):  
T. Mamatov ◽  
R. Sabirova ◽  
D. Barakaev
Keyword(s):  
Fractional Derivative ◽  
Fractional Differentiation ◽  
Hölder Condition ◽  
Hölder Spaces ◽  
Main Interest ◽  
Hölder Class ◽  
Holder Class ◽  
Function Of Two Variables ◽  
Holder Spaces

We study mixed fractional derivative in Marchaud form of function of two variables in Hölder spaces of different orders in each variables. The main interest being in the evaluation of the latter for the mixed fractional derivative in the cases Hölder class defined by usual Hölder condition

Stability and resonance conditions of second-order fractional systems

2016 ◽  
Vol 24 (4) ◽  
pp. 659-672 ◽  
Author(s):  
Elena Ivanova ◽  
Xavier Moreau ◽  
Rachid Malti
Keyword(s):  
Second Order ◽  
Damping Factor ◽  
Fractional Differentiation ◽  
Resonance Amplitude ◽  
Fractional Systems ◽  
Integral Number ◽  
At Resonance ◽  
Fractional System ◽  
The Stability ◽  
Normalized Gain

The interest of studying fractional systems of second order in electrical and mechanical engineering is first illustrated in this paper. Then, the stability and resonance conditions are established for such systems in terms of a pseudo-damping factor and a fractional differentiation order. It is shown that a second-order fractional system might have a resonance amplitude either greater or less than one. Moreover, three abaci are given allowing the pseudo-damping factor and the differentiation order to be determined for, respectively, a desired normalized gain at resonance, a desired phase at resonance, and a desired normalized resonant frequency. Furthermore, it is shown numerically that the system root locus presents a discontinuity when the fractional differentiation order is an integral number.

scholarly journals FRACTIONAL DIFFERENTIATION OF THE PRODUCT OF APPELL FUNCTION F3AND MULTIVARIABLE H-FUNCTIONS

2016 ◽  
Vol 31 (1) ◽  
pp. 115-129 ◽  
Author(s):  
Junesang Choi ◽  
Jitendra Daiya ◽  
Dinesh Kumar ◽  
Ram Kishore Saxena
Keyword(s):  
Fractional Differentiation ◽  
Appell Function

scholarly journals RF and microwave fractional differentiation with transversal filters using a soliton crystal microcomb multiwavelength source

2020 ◽  
Author(s):  
David Moss ◽  
Arnan Mitchell ◽  
Roberto Morandotti ◽  
xingyuan xu
Keyword(s):  
High Performance ◽  
Free Spectral Range ◽  
Fractional Differentiation ◽  
Temporal Response ◽  
Pulse Input ◽  
Transversal Filters ◽  
Multi Wavelength ◽  
Fractional Orders ◽  
Fractional Differentiator ◽  
Good Agreement

We report a photonic radio frequency (RF) fractional differentiator based on an integrated Kerr micro-comb source. The micro-comb source has a free spectral range (FSR) of 49 GHz, generating a large number of comb lines that serve as a high-performance multi-wavelength source for the differentiator. By programming and shaping the comb lines according to calculated tap weights, arbitrary fractional orders ranging from 0.15 to 0.90 are achieved over a broad RF operation bandwidth of 15.49 GHz. We experimentally characterize the frequency-domain RF amplitude and phase response as well as the temporal response with a Gaussian pulse input. The experimental results show good agreement with theory, confirming the effectiveness of our approach towards high-performance fractional differentiators featuring broad processing bandwidth, high reconfigurability, and potentially reduced sized and cost.

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