Temat: fractional - Prolib Integro

Skocz do pozycji: 1.

Tytuł:: Finite length triple estimation algorithm and its application to gyroscope mems noise identification
Autorzy:: Macias, Michał
Sierociuk, Dominik
Tematy:: fractional calculus
fractional Kalman filter
estimation of fractional order systems
fractional order noise; Pokaż więcej
Wydawca:: Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
Powiązania:: https://bibliotekanauki.pl/articles/2204616.pdf Link otwiera się w nowym oknie
Opis:: The noises associated with MEMS measurements can significantly impact their accuracy. The noises characterised by random walk and bias instability errors strictly depend on temperature effects that are difficult to specify during direct measurements. Therefore, the paper aims to estimate the fractional noise dynamics of the stationary MEMS gyroscope based on finite length triple estimation algorithm (FLTEA). The paper deals with the state, order and parameter estimation of fractional order noises originating from the MEMS gyroscope, being part of the popular Inertial Measurement Unit denoted as SparkFun MPU9250. The noise measurements from , and gyroscope axes are identified using a modified triple estimation algorithm (TEA) with finite approximation length. The TEA allows a simultaneous estimation of the state, order and parameter of fractional order systems. Moreover, as it is well-known that the number of samples in fractional difference approximations plays a key role, we try to show the influence of applying the TEA with various approximation length constraints on final estimation results. The validation of finite length TEA in the noise estimation process coming from MEMS gyroscope has been conducted for implementation length reduction achieving 50% of samples needed to estimate the noise with no implementation losses. Additionally, the capabilities of modified TEA in the analysis of fractional constant and variable order systems are confirmed in several numerical examples.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: On fractional random differential equations with delay
Autorzy:: Vu, H.
Phung, N. N.
Phuong, N.
Tematy:: sample path fractional integral
sample path fractional derivative
fractional differential equations
sample fractional random differential equations
Caputo fractional derivative
delay; Pokaż więcej
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Powiązania:: https://bibliotekanauki.pl/articles/254723.pdf Link otwiera się w nowym oknie
Opis:: In this paper, we consider the existence and uniqueness of solutions of the fractional random differential equations with delay. Moreover, some kind of boundedness of the solution is proven. Finally, the applicability of the theoretical results is illustrated with some real world examples.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: Existence of a solution for the fractional forced pendulum
Autorzy:: Torres, C.
Tematy:: fractional calculus
fractional boundary value problem
mountain pass theorem
fractional space; Pokaż więcej
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Powiązania:: https://bibliotekanauki.pl/articles/122603.pdf Link otwiera się w nowym oknie
Opis:: In this work we study the fractional forced pendulum equation with combined fractional derivatives - _tD^α_T ₀D^α_t u( t ) + g ( u ( t )) = f ( t ), t ∈ ( 0, T ) ( 0. 1 ) u ( 0 ) = u ( T ) = 0 where ½ < α < 1, g ∈ C ( R, R ), bounded f ∈ C [ 0, T ]. Using minimization techniques form variational calculus we show that ( 0. 1 ) has a nontrivial solution.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: Analysis of linear continuous-time systems by the use of the conformable fractional calculus and Caputo
Autorzy:: Piotrowska, E.
Tematy:: conformable fractional derivative
fractional electrical circuit
different fractional order system; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Czytelnia Czasopism PAN
Powiązania:: https://bibliotekanauki.pl/articles/141097.pdf Link otwiera się w nowym oknie
Opis:: The paper presents general solutions for fractional state-space equations. The analysis of the fractional electrical circuit in the transient state is described by the equation of the state and space equations. The results are presented for the voltage of a capacitor and current in a coil, for different alpha values. The Caputo and conformable fractional derivative definitions have been considered. At the end, the results have been obtained.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 5.

Tytuł:: Existence results for random fractional differential equations
Autorzy:: Lupulescu, V.
O’Regan, D.
Rahman ur, G.
Tematy:: random fractional differential equations
fractional integral
Caputo fractional derivative
existence; Pokaż więcej
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Powiązania:: https://bibliotekanauki.pl/articles/255930.pdf Link otwiera się w nowym oknie
Opis:: In this paper, an existence result for a random fractional differential equation is established under a Carathéodory condition. Existence results for extremal random solutions are also proved. Finally, an existence and uniqueness result is given.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 6.

Tytuł:: Formulation of the simple Markovian model using fractional calculus approach and its application to analysis of queue behavior of severe patients
Autorzy:: Dhar, Soma
Mahanta, Lipi B.
Das, Kishore Kumar
Tematy:: fractional order
arrival rate
patients
fractional calculus; Pokaż więcej
Wydawca:: Główny Urząd Statystyczny
Powiązania:: https://bibliotekanauki.pl/articles/1359228.pdf Link otwiera się w nowym oknie
Opis:: In this paper, we introduce a fractional order of a simple Markovian model where the arrival rate of the patient is Poisson, i.e. independent of the patient size. Fraction is obtained by replacing the first order time derivative in the difference differential equations which govern the probability law of the process with the Mittag-Leffler function. We derive the probability distribution of the number N(t) of patients suffering from severe disease at an arbitrary time t. We also obtain the mean size (number) of the patients suffering from severe disease waiting for service at any given time t, in the form of E ν 0.5,0.5 (t), for different fractional values of server activity status, ν = 1,0.95,0.90 and for arrival rates α = β = 0.5. A numerical example is also evaluated and analysed by using the simple Markovian model with the help of simulation techniques.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 7.

Tytuł:: Analysis of fractional electrical circuit with rectangular input signal using Caputo and conformable derivative definitions
Autorzy:: Piotrowska, E.
Tematy:: fractional order system
Caputo definition
conformable fractional definition
fractional electrical circuit; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Czytelnia Czasopism PAN
Powiązania:: https://bibliotekanauki.pl/articles/140842.pdf Link otwiera się w nowym oknie
Opis:: An analysis of a given electrical circuit using a fractional derivative. The statespace equation was developed. The dynamics of tensions described by Kirchhoff’s laws equations. The paper used the definition of the integral derivative Caputo and CDF conformable fractional definition. An electrical circuit solution using Caputo and CDF definitions for rectangular with zero initial conditions was developed. The results obtained using the Caputo and CDF definitions were compared. The solutions are shown for capacitor voltages, for fractional derivative orders of 0.6, 0.8, 1. The results were compared using graphs.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 8.

Tytuł:: Fractional Kalman Filter algorithms for correlated system and measurement noises
Autorzy:: Sierociuk, D.
Tematy:: fractional order calculus
discrete fractional state-space systems
fractional Kalman filter; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Powiązania:: https://bibliotekanauki.pl/articles/206137.pdf Link otwiera się w nowym oknie
Opis:: The paper presents a generalization of the Fractional Kalman Filter to a case when correlated system and measurement noises appear. The algorithm proposed is derived in detail for a linear generalized discrete fractional order state-space system for both constant and variable order cases. In order to present the efficiency of the proposed algorithm, results of numerical simulations are presented. Results of numerical experiments are compared with the effect of estimation obtained when using the traditional Fractional Kalman Filter algorithm.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 9.

Tytuł:: Fractional Integral Approximation and Caputo Derivatives with Modification of Trapezoidal Rule
Autorzy:: Pandiangan, Naomi
Johar, Dwindi
Purwani, Sri
Tematy:: Caputo fractional derivative
Fractional integral
Modified trapezoidal rule
Rieman Liouville fractional integral; Pokaż więcej
Wydawca:: Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Powiązania:: https://bibliotekanauki.pl/articles/1193326.pdf Link otwiera się w nowym oknie
Opis:: In classical calculus, a function can be derived or integrated as many as natural numbers. Then a question arises regarding the fractional order of derivatives and integrals. There is a development of classical calculus called fractional calculus. Fractional calculus may be a department of science that amplifies the orders of derivatives and integrals into the order of rational numbers or even real numbers. The difficulty of finding solutions analytically for a complicated function of fractional integrals or fractional derivatives often occurs. In this paper, we will solve Rieman Liouville's fractional integral and Caputo's fractional derivative analytically using the trapezoidal rule modification method. Trapezoidal method is an approximation method that is resulted from the linear interpolation function. In this paper, we will find numerical simulations with modified trapezoidal method, to estimate some functions, and the results will be compared with previous research related to the Rieman Liouville fractional integral approximation and the Caputo fractional derivative. The result from simulation find that modified trapezoidal can approximate Caputo fractional derivative by replace α with -α and Quadratic schemes method is the best method to approximate Rieman Liouville fractional integral and Caputo fractional derivative.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 10.

Tytuł:: New perspectives of analog and digital simulations of fractional order systems
Autorzy:: Charef, A.
Charef, M.
Djouambi, A.
Voda, A.
Tematy:: adjustable fractional operators
Charef approximation
fractional differential equation
ractional integrator
fractional systems; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Czytelnia Czasopism PAN
Powiązania:: https://bibliotekanauki.pl/articles/229183.pdf Link otwiera się w nowym oknie
Opis:: In the recent decades, fractional order systems have been found to be useful in many areas of physics and engineering. Hence, their efficient and accurate analog and digital simulations and numerical calculations have become very important especially in the fields of fractional control, fractional signal processing and fractional system identification. In this article, new analog and digital simulations and numerical calculations perspectives of fractional systems are considered. The main feature of this work is the introduction of an adjustable fractional order structure of the fractional integrator to facilitate and improve the simulations of the fractional order systems as well as the numerical resolution of the linear fractional order differential equations. First, the basic ideas of the proposed adjustable fractional order structure of the fractional integrator are presented. Then, the analog and digital simulations techniques of the fractional order systems and the numerical resolution of the linear fractional order differential equation are exposed. Illustrative examples of each step of this work are presented to show the effectiveness and the efficiency of the proposed fractional order systems analog and digital simulations and implementations techniques
Dostawca treści:: Biblioteka Nauki

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