Quantum Calculus Approach to the Dual Number Sequences

Source abstract

In recent years, many researchers have focused on the chaotic dynamics of quantum calculus, which arises in a variety of areas including the study of fractals, multi-fractal measures, combinatorics and special functions. In this paper, owing to some useful -calculus notations, we consider the sequence of -Fibonacci dual number and -Lucas dual number with a different perspective and we present some formulas, facts, and properties about these number sequences. After that, some fundamental identities are shown, such as D’ocagnes, Cassini, Catalan, and Binet formulas and relations of the q-dual number sequences, and described the new dual functions called -dual Fibonacci function sequences. Then, we provide some properties for these function sequences.