The Delta-nabla Calculus of Variations for Composition Functionals on Time Scales

Abstract

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.

This is a preprint of a paper whose final and definite form will be published in International Journal of Difference Equations (http://campus.mst.edu/ijde). Submitted Aug 27, 2012; Revised Nov 14, 2012; Accepted Nov 15, 2012

References in corpus (1)

• Calculus of Variations on Time Scales with Nabla Derivatives

Cited by in corpus (4)

• A Fractional Calculus on Arbitrary Time Scales: Fractional Differentiation and Fractional Integration
• Nonsymmetric and Symmetric Fractional Calculi on Arbitrary Nonempty Closed Sets
• Necessary condition for an Euler-Lagrange equation on time scales
• An Inverse Problem of the Calculus of Variations on Arbitrary Time Scales