Calculus of variations establishes a framework to determine the extrema of functionals—mappings from functions to real numbers—which has been pivotal in elucidating natural principles such as the ...

Fractional Brownian motion (FBM) with Hurst parameter index between 0 and 1 is a stochastic process originally introduced by Kolmogorov in a study of turbulence. Many other applications have ...

The first variational problem, necessary conditions. Euler's equation. Generalization to dependent and independent variables. Constraints and Lagrange multipliers. Application to dynamics and ...

Poincaré made the first attempt in 1896 on applying variational calculus to the three-body problem and observed that collision orbits do not necessarily have higher values of action than classical ...