Geodesic
A theory of linear differential equations with fractional derivatives
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 37 (2012) no. 1.

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We give the existence of solutions to the linear differential equation with fractional derivatives which are real numbers and two different types of initial conditions. Relations between these initial conditions is considered. 
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     title = {A theory of linear differential equations with fractional derivatives},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
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T. M. Atanacković; S. Pilipović; B. Stanković. A theory of linear differential equations with fractional derivatives. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 37 (2012) no. 1. http://geodesic.mathdoc.fr/item/BASS_2012_37_1_a4/