Fractional variational calculus with classical and combined Caputo derivatives - Odzijewicz, T.
We give a proper fractional extension of the classical calculus of variations by considering variational functionals with a Lagrangian depending on a combined Caputo fractional derivative and the classical derivative. EulerLagrange equations to the basic and isoperimetric problems as well as transversality conditions are proved. © 2011 Elsevier Ltd. All rights reserved.