The power quantum calculus and variational problems

Abstract

We introduce the power difference calculus based on the operator $D_{n,q}f(t)=\frac{f(q{t}^n)-f(t)}{q{t}^n-t}$, 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.

Submitted 04-Jan-2011; revised 30-Jun-2011; accepted 01-Jul-2011; for publication in Dynamics of Continuous, Discrete and Impulsive Systems, Series B (DCDIS-B)

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Cited by in corpus (4)

• Hahn's Symmetric Quantum Variational Calculus
• $p$-variational Calculus
• A study on partial dynamic equation on time scales involving derivatives of polynomials
• Helmholtz theorem for nondifferentiable Hamiltonian systems in the framework of Cresson's quantum calculus