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arXiv · 1107.0344

The power quantum calculus and variational problems

Khaled A. Aldwoah·Agnieszka B. Malinowska·Delfim F. M. Torres
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Abstract

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 $0<q<1$. Properties of the new operator and its inverse --- the $d_{n,q}$ integral --- are proved. As an application, we consider power quantum Lagrangian systems and corresponding $n,q$-Euler--Lagrange equations.

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Khaled A. Aldwoah, Agnieszka B. Malinowska, Delfim F. M. Torres. 2011-07-01. The power quantum calculus and variational problems. https://arxiv.org/abs/1107.0344

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