Variational calculus on \(q\)-nonuniform lattices (Q1779346)

The main aim of the present paper is to present the \(q\)-version of the variational calculus in the general non-uniform lattices (non \(q\)-linear lattices). In fact this paper is the logical continuation of the preceding paper ``Variational \(q\)-calculus'' [J. Math. Anal. Appl. 289, No. 2, 650--665 (2004; Zbl 1043.49001)] by the same author. In this paper the author obtains the \(q\)-analog of the Euler-Lagrange equation for non-uniform lattices and applies this to several problems as the isoperimetric, Lagrange and the optimal control problems on non-uniform lattices.