Exact solutions of simple variational fractional equations on a finite time interval

Simple variational equation containing sum of left-sided and right-sided fractional derivatives is solved. The proposed method includes transformation of the operator of the equation to equivalent Riesz potential and application of composition rules for fractional integrals and derivatives. The general solution is explicitly derived for the homogeneous case and appears to be linear combination of Fox-Wright functions. The conditions of boundedness and continuity for these solutions are studied. Then the nonhomogeneous case is also discussed and solutions in explicit form are derived. As an example the case when order of fractional operators is alpha isin (0, 1) cup (1, 2) is described in detail.