Existence of Minimizers for Fractional Variational Problems Containing   Caputo Derivatives
  We study dynamic minimization problems of the calculus of variations with Lagrangian functionals containing Riemann-Liouville fractional integrals, classical and Caputo fractional derivatives. Under assumptions of regularity, coercivity and convexity, we prove existence of solutions. 
Lo\"ic Bourdin, Tatiana Odzijewicz, Delfim F. M. Torres
math.OC