On exact solutions of a class of fractional Euler-Lagrange equations
نویسندگان
چکیده
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 aD α t x(t)) and 0 < α < 1, such that the following is the corresponding Euler-Lagrange tD α b ( c aD α t )x(t) + b(t, x(t))( c aD α t 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 tD α b ( c aD α t x(t)) = λx(t), (λ ∈ R) (2) tD α b ( c aD α t x(t)) + g(t) c aD α t x(t) = f(t), (3) where g(t) and f(t) are suitable functions.
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