Geodesic
Generalized Laplace transform of locally integrable functions defined on $[0,\infty)$
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 42 (2017) no. 1 
Bogoljub Stanković. Generalized  Laplace transform of locally integrable functions defined on $[0,\infty)$. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 42 (2017) no. 1. http://geodesic.mathdoc.fr/item/BASS_2017_42_1_a3/
@article{BASS_2017_42_1_a3,
     author = {Bogoljub Stankovi\'c},
     title = {Generalized  {Laplace} transform of locally integrable functions defined on $[0,\infty)$},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {41 - 52},
     year = {2017},
     volume = {42},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/BASS_2017_42_1_a3/}
}
TY  - JOUR
AU  - Bogoljub Stanković
TI  - Generalized  Laplace transform of locally integrable functions defined on $[0,\infty)$
JO  - Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles
PY  - 2017
SP  - 41 
EP  -  52
VL  - 42
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/BASS_2017_42_1_a3/
ID  - BASS_2017_42_1_a3
ER  - 
%0 Journal Article
%A Bogoljub Stanković
%T Generalized  Laplace transform of locally integrable functions defined on $[0,\infty)$
%J Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles
%D 2017
%P 41 - 52
%V 42
%N 1
%U http://geodesic.mathdoc.fr/item/BASS_2017_42_1_a3/
%F BASS_2017_42_1_a3

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

In $[$Bull. Cl. Sci. Math. Nat. Sci. Math. {\bf40} $(2015),\ 99-113]$ we defined the Laplace transform on a bounded interval $[0,b]$, denoted by $^0{\cal L}$, using some ideas of H. Komatsu $[$J. Fac. Sci. Univ. Tokyo, IA, {\bf34} {\rm(1987), 805--820]} and $[$Structure of solutions of differential equations $($Katata/Kyoto, $1995)$, pp. {\rm 227--252}, World Sci. Publishing, River Edge, NJ, {\rm1996]}. %(\cite{Kom} and \cite{Kom1}). We use this definition to extend it to the space of locally integrable functions defined on $[0,\infty)$, which is a wider class then functions $L$ used by G. Doetsch $[$Handbuch der Lalace-Transformation I, Basel -- Stuttgart, $1950-1956$, p.~$32]$. %(\cite{Do}, I, p.~32). As an application we give solutions of integral equations of the convolution type, defined on a bounded interval, or on the half-axis as well, and of equations with fractional derivatives.