Baleanu, DumitruBaleanu, DumitruTrujillo, Juan J.2020-04-062020-04-062008Baleanu, Dumitru; Trujillo, Juan J., "On exact solutions of a class of fractional Euler-Lagrange equations", Nonlinear Dynamics, Vol.52, No.4, pp.331-335, (2008).0924-090Xhttps://hdl.handle.net/20.500.12416/2938In 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 D-c(a)t(alpha) x(t)) and 0 < alpha < 1, such that the following is the corresponding Euler-Lagrange D-t(b)alpha(D-c(a)t(alpha))x(t) + b(t, x(t)) ((c)(a)D(t)(alpha)x(t)) + f(t, x(t)) = 0. (1) At last, exact solutions for some Euler-Lagrange equations are presented. In particular, we consider the following equations D-t(b)alpha(D-c(a)t(alpha))x(t) = lambda x(t) (lambda is an element of R), (2) D-t(b)alpha(D-c(a)t(alpha))x(t) + g(t) D-c(a)t(alpha) x(t) = f(t), (3)eninfo:eu-repo/semantics/closedAccessFractional CalculusDifferential Equations Of Fractional OrderFractional Variational CalculusArticle52433133510.1007/s11071-007-9281-7