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.
Acknowledgements
This work is part of first author’s PhD, which is carried out at the University of Aveiro under the Doctoral Programme Mathematics and Applications of Universities of Aveiro and Minho. The authors are grateful to three referees for valuable remarks and comments, which significantly contributed to the quality of the paper.
Notes
No potential conflict of interest was reported by the author(s).