Geodesic
Laplace transform of functions defined on a bounded interval
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 40 (2015), p. 99 .

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Laplace transform $\dot{\mathcal L}$ for functions belonging to $L[0,b], \; 0 b \infty$ is defined. This definition is given by using the idea 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]}. for Laplace hyperfunctions. As an application of $\dot{\mathcal L}$ we solve an equation with fractional derivative and an integral equation of the first kind of convolution type.
Classification : 46F12
Keywords: space of locally integrable functions, Laplace transform of functions belonging to $L[0;b];\;0 
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Bogoljub Stanković. Laplace transform of functions defined on a bounded interval. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 40 (2015), p. 99 . http://geodesic.mathdoc.fr/item/BASS_2015_40_a6/