The power quantum calculus and variational problems

Details The power quantum calculus and variational problems The power quantum calculus and variational problems

2011-07-01

arxiv.org/abs/1107.0344v1

Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 19 (2012), no 1-2, 93--116

Mathematics

Optimization and Control

Submitted 04-Jan-2011; revised 30-Jun-2011; accepted 01-Jul-2011; for publication in Dynamics of Continuous, Discrete and Impu

Scientific paper

We introduce the power difference calculus based on the operator $D_{n,q}
f(t) = \frac{f(qt^n)-f(t)}{qt^n -t}$, where $n$ is an odd positive integer and
$0integral --- are proved. As an application, we consider power quantum
Lagrangian systems and corresponding $n,q$-Euler--Lagrange equations.

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