Geodesic
A general method to solve fractional differential equations on $R$
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 35 (2010) no. 1 
B. Stanković. A general method to solve fractional  differential  equations on $R$. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 35 (2010) no. 1. http://geodesic.mathdoc.fr/item/BASS_2010_35_1_a3/
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     title = {A general method to solve fractional  differential  equations on $R$},
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     pages = {49 - 63},
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Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Linear differential equations with constant coefficients and Riemann-Liouville fractional derivatives defined on the real axis are analysed in a subspace of tempered distributions. This method can also give the classical solutions.