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Wyszukujesz frazę "operator Caputo" wg kryterium: Temat


Wyświetlanie 1-12 z 12
Tytuł:
The positivity of the fractional order model of a two-dimensional temperature field
Autorzy:
Oprzędkiewicz, Krzysztof
Powiązania:
https://bibliotekanauki.pl/articles/27311454.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Czasopisma i Monografie PAN
Tematy:
heat transfer equation
fractional order state equation
Caputo operator
positivity
thermal camera
non-integer order systems
równanie wymiany ciepła
równanie stanu rzędu ułamkowego
operator Caputo
kamera termowizyjna
systemy niecałkowitego rzędu
dodatniość
Opis:
The paper presents analysis of the positivity for a two-dimensional temperature field. The process under consideration is described by the linear, infinite-dimensional, noninteger order state equation. It is derived from a two-dimensional parabolic equation with homogenous Neumann boundary conditions along all borders and homogenous initial condition. The form of control and observation operators is determined by the construction of a real system. The internal and external positivity of the model are associated to the localization of heater and measurement. It has been proven that the internal positivity of the considered system can be achieved by the proper selection of attachment of a heater and place of a measurement as well as the dimension of the finite-dimensional approximation of the considered model. Conditions of the internal positivity associated with construction of real experimental system are proposed. The postivity is analysed separately for control and output of the system. This allows one to analyse the positivity of thermal systems without explicit control. Theoretical considerations are numerically verified with the use of experimental data. The proposed results can be applied i.e. to point suitable places for measuring of a temperature using a thermal imaging camera.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2023, 71, 4; art. no. e145675
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Caputo vs. Caputo-Fabrizio operators in modeling of heat transfer process
Autorzy:
Oprzędkiewicz, K.
Mitkowski, W.
Gawin, E.
Dziedzic, K.
Powiązania:
https://bibliotekanauki.pl/articles/200001.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional order systems
Caputo operator
Caputo-Fabrizio operator
non singular kernel operator
heat transfer
simplex method
transfer ciepła
metoda simplex
system ułamkowy
pochodna Caputo
Opis:
In the paper two non-integer order, state space models of heat transfer process are compared. The first uses a known Caputo operator and the second – a new operator proposed by Caputo and Fabrizio in 2015. Both discussed models are modifications of a known, integer order, state space, semigroup model of heat transfer process. Parameters of both models were identified by means of optimization of MSE cost function with the use of simplex method, available in MATLAB. Both proposed models have been compared in the aspect of accuracy and convergence. Analytical and numerical results show that the Caputo-Fabrizio model is faster convergent and easier to implement than the Caputo model. However, its accuracy in the sense of MSE cost function is worse.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 4; 501-507
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fox H-functions as exact solutions for Caputo type mass spring damper system under Sumudu transform
Autorzy:
Qureshi, Sania
Powiązania:
https://bibliotekanauki.pl/articles/1839854.pdf
Data publikacji:
2021
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
special functions
free damped oscillations
un-damped oscillations
driven force
funkcje specjalne
operator Caputo
metoda transformacji Sumudu
transformacja całkowa Smudu
rachunek ułamkowy
Opis:
Closed form solutions for mathematical systems are not easy to find in many cases. In particular, linear systems such as the population growth/decay model, RLC circuit, mixing problems in chemistry, first-order kinetic reactions, and mass spring damper system in mechanical and mechatronic engineering can be handled with tools available in theoretical study of linear systems. One such linear system has been investigated in the present research study. The second order linear ordinary differential equation called the mass spring damper system is explored under the Caputo type differential operator while using the Sumudu integral transform. The closed form solution has been found in terms of the Fox H-function wherein different aspects of the solution can be obtained with variation in a 2 (1;2] and b 2 (0;1]: The classical mass spring damper model is retrieved for a = b = 1:
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2021, 20, 1; 83-89
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Non integer order, state space model of heat transfer process using Caputo-Fabrizio operator
Autorzy:
Oprzędkiewicz, K.
Powiązania:
https://bibliotekanauki.pl/articles/201464.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
non-integer order systems
heat transfer equation
infinite dimensional systems
fractional order state equation
Riesz operator
Caputo operator
Caputo-Fabrizio operator
systemy niecałkowitego rzędu
układ niecałkowitego rzędu
twierdzenie Riesza
pochodna Caputo
Opis:
The paper is intended to show a new state space, non integer order model of an one-dimensional heat transfer process. The proposed model derives directly from time continuous, state space semigroup model. The fractional order derivative with respect to time is by a new operator proposed by Caputo and Fabrizio, the non integer order spatial derivative is expressed by Riesz operator. The Caputo-Fabrizio operator can be directly implementated using MATLAB, because it does not require us to apply any approximation. Analytical formulae of step response are given, the system decomposition was discussed also. Main results from the paper show that the use of Caputo Fabrizio operator allows us to obtain the simple in implementation and analysis model of the considered heat transfer process. The accuracy of the proposed model in the sense of a MSE cost function is satisfying.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 3; 249-255
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Accuracy estimation of the approximated Atangana-Baleanu operator
Autorzy:
Oprzędkiewicz, Krzysztof
Mitkowski, Wojciech
Powiązania:
https://bibliotekanauki.pl/articles/122484.pdf
Data publikacji:
2019
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
Caputo operator
Mittag-Leffler function
ORA approximation
aproksymacja ORA
funkcja Mittag-Lefflera
Opis:
In the paper, the accuracy analysis of the approximation of the Atangana-Baleanu (AB) operator is presented. The AB operator is the nonsingular kernel operator proposed by Atangana and Baleanu. It is obtained by replacing the exponential function in the Caputo-Fabrizio operator by the Mittag-Leffler function. The Laplace transform of the AB operator requires approximating the factor sa. This is done using the well-known Oustaloup Recursive Approximaion (ORA) approximation. The step and frequency responses of the approximation are compared to the analytical responses. As the cost function, the FIT function available in MATLAB was applied. Results of simulations show that the use of ORA allows us to obtain the accurate approximant of the AB operator.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 4; 53-62
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the nonoscillatory behavior of solutions of three classes of fractional difference equations
Autorzy:
Grace, Said Rezk
Alzabut, Jehad
Punitha, Sakthivel
Muthulakshmi, Velu
Adiguzel, Hakan
Powiązania:
https://bibliotekanauki.pl/articles/255333.pdf
Data publikacji:
2020
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Caputo difference operator
nonoscillation criteria
fractional difference equation mathematical inequalities
Opis:
In this paper, we study the nonoscillatory behavior of three classes of fractional difference equations. The investigations are presented in three different folds. Unlike most existing nonoscillation results which have been established by employing Riccati transfor mation technique, we employ herein an easily verifiable approach based on the fractional Taylor’s difference formula, some features of discrete fractional calculus and mathematical inequalities. The theoretical findings are demonstrated by examples. We end the paper by a concluding remark.
Źródło:
Opuscula Mathematica; 2020, 40, 5; 549-568
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fractional discrete-continuous model of heat transfer process
Autorzy:
Oprzędkiewicz, Krzysztof
Dziedzic, Klaudia
Powiązania:
https://bibliotekanauki.pl/articles/1409413.pdf
Data publikacji:
2021
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
non integer order systems
heat transfer equation
finite difference
Caputo operator
positive systems
Opis:
The paper proposes a new, state space, finite dimensional, fractional order model of a heat transfer in one dimensional body. The time derivative is described by Caputo operator. The second order central difference describes the derivative along the length. The analytical formulae of the model responses are proved. The stability, convergence, and positivity of the model are also discussed. Theoretical results are verified by experiments.
Źródło:
Archives of Control Sciences; 2021, 31, 2; 287-306
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Growth of solutions of a class of linear fractional differential equations with polynomial coefficients
Autorzy:
Hamouda, Saada
Mahmoudi, Sofiane
Powiązania:
https://bibliotekanauki.pl/articles/2216191.pdf
Data publikacji:
2022
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
linear fractional differential equations
growth of solutions
Caputo fractional derivative operator
Opis:
This paper is devoted to the study of the growth of solutions of certain class of linear fractional differential equations with polynomial coefficients involving the Caputo fractional derivatives by using the generalized Wiman–Valiron theorem in the fractional calculus.
Źródło:
Opuscula Mathematica; 2022, 42, 3; 415-426
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Non integer order, state space model of heat transfer process using Atangana-Baleanu operator
Autorzy:
Oprzędkiewicz, K.
Powiązania:
https://bibliotekanauki.pl/articles/202078.pdf
Data publikacji:
2020
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
non integer order systems
heat transfer equation
infinite dimensional systems
fractional order state equation
Riesz operator
Caputo operator
Atangana-Baleanu operator
Opis:
In the paper a new, state space, non integer order model of an one-dimensional heat transfer process is proposed. The model uses a new operator with Mittag-Leffler kernel, proposed by Atangana and Beleanu. The non integer order spatial derivative is expressed by Riesz operator. Analytical formula of the step response is given, the convergence of the model is discussed too. Theoretical results are verified by experiments.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2020, 68, 1; 43-50
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Exact solutions for fractionalized second grade fluid flows with boundary slip effects
Autorzy:
Dehraj, S.
Malookani, R. A.
Aasoori, S. K.
Bhutto, G. M.
Arain, L.
Powiązania:
https://bibliotekanauki.pl/articles/1839889.pdf
Data publikacji:
2021
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
transformata Laplace'a
poślizg
płyn eksploatacyjny
second grade fluid
Caputo fractional operator
slip effects
discrete Laplace transform
Opis:
In this paper, an exact analytical solution for the motion of fractionalized second grade fluid flows moving over accelerating plate under the influence of slip has been obtained. A coupled system of partial differential equations representing the equation of motion has been re-written in terms of fractional derivatives form by using the Caputo fractional operator. The Discrete Laplace transform method has been employed for computing the expressions for the velocity field […] and the corresponding shear stress […]. The obtained solutions for the velocity field and the shear stress have been written in terms of Wright generalized hypergeometric function pqψ and are expressed as a sum of the slip contribution and the corresponding no-slip contribution. In addition, the solutions for a fractionalized, ordinary second grade fluid and Newtonian fluid in the absence of slip effect have also been obtained as special case. Finally, the effect of different physical parameters has been demonstrated through graphical illustrations.
Źródło:
International Journal of Applied Mechanics and Engineering; 2021, 26, 1; 88-103
1734-4492
2353-9003
Pojawia się w:
International Journal of Applied Mechanics and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Nonlinear Fractional Neutral Differential Equation with the ψ-Caputo Fractional Derivative
Autorzy:
Nabil, Tamer
Powiązania:
https://bibliotekanauki.pl/articles/1818657.pdf
Data publikacji:
2020
Wydawca:
Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
Tematy:
Krasnoselskii's fixed point theory
ψ − Caputo operator
neutral differential equation
ulam stability
existence of solution
teoria punktu stałego Krasnoselskiego
operator Caputa
równanie różniczkowe
stabilność Ulama
Opis:
In this article, the solvability of fractional neutral differential equation involving ψ−Caputo fractional operator is considered usinga Krasnoselskii’s fixed point approach. Also, we establish the uniquenessof the solution under certain conditions. Ulam stabilities for the proposedproblem are discussed. Finally, examples are displayed to aid the applicability of the theory results.
Źródło:
Journal of Mathematics and Applications; 2020, 43; 99--112
1733-6775
2300-9926
Pojawia się w:
Journal of Mathematics and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Mittag-Leffler stability for a Timoshenko problem
Autorzy:
Tatar, Nasser-eddine
Powiązania:
https://bibliotekanauki.pl/articles/1838213.pdf
Data publikacji:
2021
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
Caputo fractional derivative
Mittag-Leffler stability
multiplier technique
resolvent operator
Opis:
A Timoshenko system of a fractional order between zero and one is investigated here. Using a fractional version of resolvents, we establish an existence and uniqueness theorem in an appropriate space. Moreover, it is proved that lower order fractional terms (in the rotation component) are capable of stabilizing the system in a Mittag-Leffler fashion. Therefore, they deserve to be called damping terms. This is shown through the introduction of some new functionals and some fractional inequalities, and the establishment of some properties, involving fractional derivatives. In the case of different wave speeds of propagation we obtain convergence to zero.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2021, 31, 2; 219-232
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
    Wyświetlanie 1-12 z 12

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