Time scales: from Nabla calculus to Delta calculus and vice versa via duality

Abstract

In this note we show how one can obtain results from the nabla calculus from results on the delta calculus and vice versa via a duality argument. We provide applications of the main results to the calculus of variations on time scales.

arXiv commentChanged some minor typos

References in corpus (4)

• Calculus of Variations on Time Scales with Nabla Derivatives
• Higher-Order Calculus of Variations on Time Scales
• Strong Minimizers of the Calculus of Variations on Time Scales and the Weierstrass Condition
• Remarks on the calculus of variations on time scales

Cited by in corpus (10)

• Duality for the left and right fractional derivatives
• Noether's symmetry theorem for nabla problems of the calculus of variations
• Exponentials and Laplace transforms on nonuniform time scales
• Generalizing the variational theory on time scales to include the delta indefinite integral
• A General Backwards Calculus of Variations via Duality
• Existence of solutions for dynamic inclusions on time scales via duality
• A Table of Derivatives on Arbitrary Time Scales
• Non shifted calculus of variations on time scales with Nabla-differentiable Sigma
• L'Hopital-Type Rules for Monotonicity with Application to Quantum Calculus
• A study on partial dynamic equation on time scales involving derivatives of polynomials