This brief presents a general unifying perspective on the fractional calculus. It brings
together results of several recent approaches in generalizing the least action principle and
the Euler¿Lagrange equations to include fractional derivatives. The dependence of Lagrangians
on generalized fractional operators as well as on classical derivatives is considered along
with still more general problems in which integer-order integrals are replaced by fractional
integrals. General theorems are obtained for several types of variational problems for which
recent results developed in the literature can be obtained as special cases. In particular the
authors offer necessary optimality conditions of Euler¿Lagrange type for the fundamental and
isoperimetric problems transversality conditions and Noether symmetry theorems. The existence
of solutions is demonstrated under Tonelli type conditions. The results are used to prove the
existence of eigenvalues and corresponding orthogonal eigenfunctions of fractional
Sturm¿Liouville problems. Advanced Methods in the Fractional Calculus of Variations is a
self-contained text which will be useful for graduate students wishing to learn about
fractional-order systems. The detailed explanations will interest researchers with backgrounds
in applied mathematics control and optimization as well as in certain areas of physics and
engineering.
