Let us consider the following fractional problem of the

calculus of variations:

The theoretical concepts case study, analyzed in this paper on the alternative roundabouts worthiness in the way analogous to the aircraft airworthiness supporting measures effectiveness research, proves that the described

calculus of variations approach allows obtaining the objectively existing optimal values of the operational (functioning) purpose functional with the help of the specially introduced determining functions.

This assumption renders the problem (P) a simple

calculus of variations problem, which is too restrictive for this study.

>because (11) involves the constraint -x' (t)e/(e - t) [member of] [0,a], [for all]t [member of] [0, [T.sub.x]], such that (11) is still a nonstandard

calculus of variation problem.

Based on the optimal control problem of continuous systems and the

calculus of variations, the variational problem can be stated as follows.

Clarke, Functional Analysis,

Calculus of Variations and Optimal Control, Springer, London, UK, 2013.

Marzocchi, On the Euler-Lagrange equation for functional of the

Calculus of Variations without upper growth conditions, SIAM J.

We now exemplify how the expansions obtained in Section 3 are useful to approximate solutions of fractional problems of the

calculus of variations [21].

Weber: What about dynamic analysis and the

calculus of variations, did you learn about such matters from your studies in physics or did you acquire that later on?

It contains 16 papers on such topics as travel time tubes regulating transportation traffic, quadratic growth conditions in optimal control problems, optimal spatial pricing strategies with transportation costs, isoperimetric problems of the

calculus of variations on time scales, metric regular maps and regularity for constrained extremum problems, and isoperimetric problems of the

calculus of variations on time scales, to cite a few examples.

Recently several authors have contributed to the development of the

calculus of variations on time scales (for instance, see [3,11,12]).

The

calculus of variations on time scales was introduced in 2004 with the papers of Bohner [6] and Hilscher and Zeidan [15].

The

calculus of variations is generally regarded as originating with the papers of Jean Bernoulli on the problem of the brachistochrone.

Project 2:

Calculus of variations, Brachistochrone experiment and analysis of the cycloid

Expanded coverage of essential math, including integral equations,

calculus of variations, tensor analysis, and special integrals.