Quaternions : quantum calculus approach with applications

الملخص EN

In this paper we introduce two types of quaternion sequences with components including quantum integers.

we also introduce quantum quaternion polynomials.

moreover, we give some properties and identities for these quantum quaternions and polynomials.

finally, we give time evolution and rotation applications for some specific quaternion sequences.

the applications can be converted into quantum integer forms under suitable conditions with similar considerations.