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- Optimality Conditions for Fractional Variational Problems with Dependence on a Combined Caputo Derivative of Variable OrderPublication . Tavares, Dina; Almeida, Ricardo; Torres, Delfim F. M.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.