Temat: fractional difference equations - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Existence of positive solutions to a discrete fractional boundary value problem and corresponding Lyapunov-type inequalities
Autorzy:: Chidouh, A.
Torres, D. F. M.
Powiązania:: https://bibliotekanauki.pl/articles/255913.pdf
Data publikacji:: 2018
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: fractional difference equations
Lyapunov-type inequalities
fractional boundary value problems
positive solutions
Opis:: We prove existence of positive solutions to a boundary value problem depending on discrete fractional operators. Then, corresponding discrete fractional Lyapunov-type inequalities are obtained.
Źródło:: Opuscula Mathematica; 2018, 38, 1; 31-40
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

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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