On exact solutions of a class of fractional Euler–Lagrange equations

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In this paper, first a class of fractional differential equations are obtained by using the fractional variational principles. We find a fractional Lagrangian L(x(t), where acDtαx(t)) and 0<α<1, such that the following is the corresponding Euler–Lagrange

At last, exact solutions for some Euler–Lagrange equations are presented. In particular, we consider the following equations

where g(t) and f(t) are suitable functions.

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