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Fractional calculus methods and techniques are playing and important role in science and engineering. Since fractional equations are important in theory and application, in the last years, researches on fractional differential equations have achieved significant development. Recently, the study of fractional differential equations through variational methods become an important filed of study for several researches. A new research trend started to be developed, especially for fractional differential equations having both the left and right fractional derivatives, because, in general, the fixed-point theory is not a suitable tool to show existence results to this type of equations. Namely, it is not obvious to convert this type of fractional equation into an equivalent integral equation and then transformed into some fixed-point problem.