TY - JOUR
N2 - The paper is a newapproach to the Duhamel integral. It contains an overviewof 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.
L1 - http://sd.czasopisma.pan.pl/Content/121918/PDF/art04.pdf
L2 - http://sd.czasopisma.pan.pl/Content/121918
PY - 2021
IS - No 4
EP - 847
DO - 10.24425/acs.2021.139732
KW - Duhamel’s integral
KW - Duhamel’s principle
KW - Duhamel’s formula
KW - Laplace transformation
KW - semigroup of operators
KW - Leibniz integral rule
KW - Volterra integral equation
KW - Caputo fractional derivative
A1 - Różański, Michał
A1 - Sikora, Beata
A1 - Smuda, Adrian
A1 - Wituła, Roman
PB - Committee of Automatic Control and Robotics PAS
VL - vol. 31
DA - 2021.12.27
T1 - On theoretical and practical aspects of Duhamel’s integral
SP - 815
UR - http://sd.czasopisma.pan.pl/dlibra/publication/edition/121918
T2 - Archives of Control Sciences
ER -