On Transcendental Entire Solution of Ordinary and Systems of Different Genre of Fermat-type q-Shift Equations

Our paper focuses on exploring transcendental entire solutions of various types of q-shift binomial and trinomial Fermat-type equations. Additionally, we extend the investigation to simultaneous equations involving q-shift, taking into account the complexity and feasibility of analyzing these equations. We have identified and highlighted important observations that differentiate these q-shift equations from their analogous shift equations. In addition to transcendental entire solutions, we have also ventured into finding meromorphic solution for certain types of q-shift equations. To support our results and conclusions, we provide a series of examples to demonstrate the validity of our findings in terms of the transcendental entire and meromorphic solutions we have discovered.