Applications of q-Phragmén-Lindelöf Indicator to the Growth of Solutions of q-Difference Equations

Abstract This paper applies a new tool— q -Phragmén-Lindelöf Indicator, which resolves the problem of determining the growth of solutions to q -difference equations in the absence of a dominant coefficient. To the best of our knowledge, this paper presents the first time that the q -Phragmén-Lindelöf indicator is linked with complex equations and utilized to characterize the growth properties of their solutions. Our results encompass and generalize some of the earlier research findings in this area.