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 c a D α t x(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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D. Baleanu is on leave of absence from Institute of Space Sciences, P.O. BOX MG-23, 76900 Magurele-Bucharest, Romania. e-mail: email@example.com.
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Baleanu, D., Trujillo, J.J. On exact solutions of a class of fractional Euler–Lagrange equations. Nonlinear Dyn 52, 331–335 (2008). https://doi.org/10.1007/s11071-007-9281-7
- Fractional calculus
- Differential equations of fractional order
- Fractional variational calculus