The Delta-nabla Calculus of Variations for Composition Functionals on   Time Scales
  We develop the calculus of variations on time scales for a functional that is the composition of a certain scalar function with the delta and nabla integrals of a vector valued field. Euler-Lagrange equations, transversality conditions, and necessary optimality conditions for isoperimetric problems, on an arbitrary time scale, are proved. Interesting corollaries and examples are presented. 
Monika Dryl, Delfim F. M. Torres
math.OC