Differential-integral Euler-Lagrange equations.

We study the calculus of variations problem in the presence of a system of differential-integral (D-I) equations. In order to identify the necessary optimality conditions for this problem, we derive the so-called D-I Euler-Lagrange equations. We also generalize this problem to other cases, such as the case of higher orders, the problem of optimal control, and we derive the so-called D-I Pontryagin equations. In special cases, these formulations lead to classical Euler-Lagrange equations. To illustrate our results, we provide simple examples and applications such as obtaining the minimum power for an RLC circuit. [ABSTRACT FROM AUTHOR]