Search

Abstract: We introduce differential, integral, and variational delta embeddings. We prove that the integral delta embedding of the Euler–Lagrange equations and the variational delta embedding coincide on an arbitrary time scale. In particular, a new coherent embedding for the discrete calculus of variations that is compatible with the least-action principle is obtained. [Copyright &y& Elsevier]

Abstract: We prove the Euler–Lagrange delta-differential equations for problems of the calculus of variations on arbitrary time scales with delta-integral functionals depending on higher-order delta derivatives. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents the necessary and sufficient optimality conditions for problems of the fractional calculus of variations with a Lagrangian depending on the free end-points. The fractional derivatives are defined in the sense of Caputo. [Copyright &y& Elsevier]