Geodesic
An Equation With Left and Right Fractional Derivatives
Publications de l'Institut Mathématique, _N_S_80 (2006) no. 94, p. 259 .

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We consider an equation with left and right fractional derivatives and with the boundary condition $y(0)=\lim\limits_{x\to 0^+}y(x)=0$, $y(b)=\lim\limits_{x\to b^-}y(x)=0$ in the space $\mathcal{L}^1(0, b)$ and in the subspace of tempered distributions. The asymptotic behavior of solutions in the end points $0$ and $b$ have been specially analyzed by using Karamata's regularly varying functions.
DOI : 10.2298/PIM0694259S
Classification : 26A33 26A12
Keywords: Right and left Riemann--Liuville fractional derivative, Fractional differential equation, Regulary varying functions 
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     author = {B. Stankovi\'c},
     title = {An {Equation} {With} {Left} and {Right} {Fractional} {Derivatives}},
     journal = {Publications de l'Institut Math\'ematique},
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     publisher = {mathdoc},
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B. Stanković. An Equation With Left and Right Fractional Derivatives. Publications de l'Institut Mathématique, _N_S_80 (2006) no. 94, p. 259 . doi : 10.2298/PIM0694259S. http://geodesic.mathdoc.fr/articles/10.2298/PIM0694259S/

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