The object of this paper is to establish an existence result for nonlinear inequalities for not necessarily pseudomonotone maps. As a consequence of our result, we give some existence results for variational and variational-like inequalities. Keywords– Nonlinear inequalities, variational inequality problems, variational-like inequality problems, fixed points.

Abstract. The study of fractional variational problems in terms of a combined fractional Caputo derivative is introduced. Necessary optimality conditions of Euler–Lagrange type for the basic, isoperimetric, and Lagrange variational problems are proved, as well as transversality and sufficient optimality conditions. This allows to obtain necessary and sufficient Pareto optimality conditions for ...