Title: Optimality conditions for fractional variational problems with dependence on a combined Caputo derivative of variable order published at Optimization.

IPLeiria authores: Dina Tavares


Main Results:

The fractional calculus of variations is a particular topic of mathematics that involves the optimization of functionals that depend on some fractional integrals or derivatives. This subject is recent and its development is due to different applications in others areas of knowledge.

In this paper, we established necessary optimality conditions for variational problems with a Lagrangian depending on a combined Caputo derivative of non-constant fractional order (variable order). For the problem we impose a boundary condition in the initial time and the endpoint is free, so transversality conditions are proved. In the end of the paper, we considered some particular cases.

This article was developed in the Doctoral Program in Mathematics and Applications at the Universities of Aveiro and Minho.