Wszystkie pola: fractional difference equations - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Variation of constant formulas for fractional difference equations
Autorzy:: Anh, P. T.
Babiarz, A.
Czornik, A.
Niezabitowski, M.
Siegmund, S.
Powiązania:: https://bibliotekanauki.pl/articles/229367.pdf
Data publikacji:: 2018
Wydawca:: Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:: fractional difference equation
variation of constant
separation of solutions
Opis:: In this paper, we establish variation of constant formulas for both Caputo and Riemann-Liouville fractional difference equations. The main technique is the Z-transform. As an application, we prove a lower bound on the separation between two different solutions of a class of nonlinear scalar fractional difference equations.
Źródło:: Archives of Control Sciences; 2018, 28, 4; 617-633
1230-2384
Pojawia się w:: Archives of Control Sciences
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Problems in solving fractional differential equations in a microcontroller implementation of an FOPID controller
Autorzy:: Matusiak, Mariusz
Ostalczyk, Piotr
Powiązania:: https://bibliotekanauki.pl/articles/140935.pdf
Data publikacji:: 2019
Wydawca:: Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:: fractional calculus
Grünwald-Letnikov fractional-order backward difference
FOPID
hardware implementation
Opis:: The article focuses on the fractional-order backward difference, sum, linear time-invariant equation analysis, and difficulties of the fractional calculus microcontroller implementation with regard to designing a fractional-order proportional integral derivative (FOPID) controller. In opposite to the classic proportional integral derivative (PID), the FOPID controller is defined by five independent parameters. Hence, it is more customizable and, potentially, more precise on condition that the values of fractional integration and differentiation orders are properly selected. However, a number of operations and the time required to calculate the output signal continuously increase. This can be a significant problem considering the limitations of a microcontroller, including memory size and a constant sampling time of the set-up analog-to-digital (ADC) converters. In the article, three solutions are considered, and results obtained in the experiments are presented.
Źródło:: Archives of Electrical Engineering; 2019, 68, 3; 565-577
1427-4221
2300-2506
Pojawia się w:: Archives of Electrical Engineering
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: The implicit numerical method for the one-dimensional anomalous subdiffusion equation with a nonlinear source term
Autorzy:: Błasik, Marek
Powiązania:: https://bibliotekanauki.pl/articles/2086846.pdf
Data publikacji:: 2021
Wydawca:: Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:: fractional derivative
fractional integral
integro-differential equations
numerical method
finite difference method
pochodna ułamkowa
całkowanie ułamkowe
równanie całkowo-różniczkowe
metoda numeryczna
metoda elementów skończonych
Opis:: In the paper, the numerical method of solving the one-dimensional subdiffusion equation with the source term is presented. In the approach used, the key role is played by transforming of the partial differential equation into an equivalent integro-differential equation. As a result of the discretization of the integro-differential equation obtained an implicit numerical scheme which is the generalized Crank-Nicolson method. The implicit numerical schemes based on the finite difference method, such as the Carnk-Nicolson method or the Laasonen method, as a rule are unconditionally stable, which is their undoubted advantage. The discretization of the integro-differential equation is performed in two stages. First, the left-sided Riemann-Liouville integrals are approximated in such a way that the integrands are linear functions between successive grid nodes with respect to the time variable. This allows us to find the discrete values of the integral kernel of the left-sided Riemann-Liouville integral and assign them to the appropriate nodes. In the second step, second order derivative with respect to the spatial variable is approximated by the difference quotient. The obtained numerical scheme is verified on three examples for which closed analytical solutions are known.
Źródło:: Bulletin of the Polish Academy of Sciences. Technical Sciences; 2021, 69, 6; e138240, 1--9
0239-7528
Pojawia się w:: Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:: Biblioteka Nauki

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