Geodesic
Weak solutions to differential equations with left and right fractional derivatives defined on ${\Bbb R}$
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 34 (2009) no. 1 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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We treat linear differential equations containing both left and right Riemann-Liouville fractional derivatives arising from fractional variational problems. We use the Fourier transform method to obtain weak solution to the problem. Regularity of such solution is examined and the conditions for the existence of classical solution are stated. 
@article{BASS_2009_34_1_a3,
     author = {T. M. Atanackovi\'c and S. Pilipovi\'c and B. Stankovi\'c},
     title = {Weak solutions to  differential equations with left and right fractional  derivatives defined on ${\Bbb R}$},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {75 - 88},
     year = {2009},
     volume = {34},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/BASS_2009_34_1_a3/}
}
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T. M. Atanacković; S. Pilipović; B. Stanković. Weak solutions to  differential equations with left and right fractional  derivatives defined on ${\Bbb R}$. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 34 (2009) no. 1. http://geodesic.mathdoc.fr/item/BASS_2009_34_1_a3/