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://www.czasopisma.pan.pl/Content/121918/PDF/art04.pdf L2 - http://www.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://www.czasopisma.pan.pl/dlibra/publication/edition/121918 T2 - Archives of Control Sciences ER -