A new approach on fractional variational problems and Euler-Lagrange equations

摘要

In this paper we generalize fractional variational problems in [a, b]. We allow for the possibility that functions in the space of solution for the optimization problem can blow up at boundary points. The appropriate fractional derivative spaces are introduced and a compact embedding theorem demonstrated. We prove the existence of minimizers for the variational problems which satisfy the Euler- Lagrange equations with Riemann- Liouville boundary conditions. Our method is based on the fractional calculus of variations. An example is given to illustrate the results. (C) 2014 Elsevier B.V. All rights reserved.