Fractional calculus of variations for a combined Caputo derivative

Abstract

Abstract We generalize the fractional Caputo derivative to the fractional derivative C D γα,β, which is a convex combination of the left Caputo fractional derivative of order α and the right Caputo fractional derivative of order β. The fractional variational problems under our consideration are formulated in terms of C D γα,β. The Euler-Lagrange equations for the basic and isoperimetric problems, as well as transversality conditions, are proved.