Much recent research activity has focused on the theory and application of quantum calculus. This branch of mathematics continues to find new and useful applications and there is much promise left for investigation into this field. We present a formulation of dynamic programming grounded in the quantum calculus. Our results include the standard dynamic programming induction algorithm which can be interpreted as the Hamilton-Jacobi-Bellman equation in the quantum calculus. Furthermore, we show that approximate dynamic programming in quantum calculus is tenable by laying the groundwork for the backpropagation algorithm common in neural network training. In particular, we prove that the chain rule for ordered derivatives, fundamental to backpropagation, is valid in quantum calculus. In doing this we have connected two major fields of research.

Meeting Name

IEEE International Joint conference on Neural Networks, 2008. IJCNN 2008. (IEEE World Congress on Computational Intelligence)


Electrical and Computer Engineering

Second Department

Computer Science

Keywords and Phrases

Backpropagation; Dynamic Equations; Dynamic Programming; Quantum Calculus; Time Scales

Document Type

Article - Conference proceedings

Document Version

Final Version

File Type





© 2008 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Jun 2008