- Tytuł:
- On theoretical and practical aspects of Duhamel’s integral
- Autorzy:
-
Różański, Michał
Sikora, Beata
Smuda, Adrian
Wituła, Roman - Powiązania:
- https://bibliotekanauki.pl/articles/2083463.pdf
- Data publikacji:
- 2021
- Wydawca:
- Polska Akademia Nauk. Czytelnia Czasopism PAN
- Tematy:
-
Duhamel’s integral
Duhamel’s principle
Duhamel’s formula
Laplace transformation
semigroup of operators
Leibniz integral rule
Volterra integral equation
Caputo fractional derivative - Opis:
- The paper is a new approach to the Duhamel integral. It contains an overview of formulas and applications of Duhamel’s integral as well as a number of new results on the Duhamel integral and principle. Basic definitions are recalled and formulas for Duhamel’s integral are derived via Laplace transformation and Leibniz integral rule. Applications of Duhamel’s integral for solving certain types of differential and integral equations are presented. Moreover, an interpretation of Duhamel’s formula in the theory of operator semigroups is given. Some applications of Duhamel’s formula in control systems analysis are discussed. The work is also devoted to the usage of Duhamel’s integral for differential equations with fractional order derivative.
- Źródło:
-
Archives of Control Sciences; 2021, 31, 4; 815-847
1230-2384 - Pojawia się w:
- Archives of Control Sciences
- Dostawca treści:
- Biblioteka Nauki
Artykuł