Weak solutions to differential equations with left and right fractional derivatives defined on ${\Bbb R}$

T. M.,Atanacković, S.,Pilipović, B.,Stanković

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.