Tavares, DinaAlmeida, RicardoTorres, Delfim F. M.2018-06-282018-06-282017-03-27http://hdl.handle.net/10400.8/3312We study fractional variational problems of Herglotz type of variable order. Necessary optimality conditions, described by fractional differential equations depending on a combined Caputo fractional derivative of variable order, are proved. Two different cases are considered: the fundamental problem, with one independent variable, and the general case, with several independent variables. We end with some illustrative examples of the results of the paper.engFractional calculusVariable orderHerglotz variational problemsjournal article10.3934/dcdss.2018009