Optimality Conditions for Fractional Variational Problems with Dependence on a Combined Caputo Derivative of Variable Order

Abstract

We establish necessary optimality conditions for variational problems with a Lagrangian depending on a combined Caputo derivative of variable fractional order. The endpoint of the integral is free, and thus transversality conditions are proved. Several particular cases are considered illustrating the new results.

This is a preprint of a paper whose final and definite form will be published in Optimization, ISSN 0233-1934 (Print), 1029-4945 (Online). Submitted 05-Feb-2014; revised 16-May, 14-July and 16-Dec-2014; accepted 08-Jan-2015

References in corpus (2)

• Calculus of variations with fractional derivatives and fractional integrals
• Fractional Variations for Dynamical Systems: Hamilton and Lagrange Approaches