NECESSARY AND SUFFICIENT OPTIMALITY CONDITIONS FOR FVPS WITH GENERALIZED BOUNDARY CONDITIONS

Abstract

This paper presents the necessary and sufficient optimality conditions for fractional variational problems with generalized boundary conditions. The Lagrangian that we consider depends on left Caputo fractional derivatives of order $\alpha$ and which also depends on the boundary points $y(a)$ and $y(b)$. The initial point $y(a)$, the terminal time $b$, and the end point $y(b)$ may be not specified. Examples are presented to demonstrate the application of the formulations.