Variational \(q\)-calculus. (English) Zbl 1043.49001

Summary: We propose \(q\)-versions of some basic concepts of continuous variational calculus such as the Euler–Lagrange equation and its applications to the isoperimetric, Lagrange and optimal control problems (“the maximum principle”), and also to the Hamilton systems and commutation equations.


49J05 Existence theories for free problems in one independent variable
49K05 Optimality conditions for free problems in one independent variable
39A12 Discrete version of topics in analysis
39A13 Difference equations, scaling (\(q\)-differences)
33D90 Applications of basic hypergeometric functions
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