| Summary: | The aim of this work is to study several problems of the calculus of variations, where the dynamics of the state function is given by a generalized fractional derivative. This derivative combines two well-known concepts: fractional derivative with respect to another function and fractional derivative of variable order. We present the Euler–Lagrange equation, which is a necessary condition that every optimal solution of the problem must satisfy. Other problems are also studied: with integral and holonomic constraints, with higher order derivatives, and the Herglotz variational problem.
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