Comparative growth properties of special type of differential polynomial generated by entire and meromorphic functions on the basis of their generalized order α,β

In this paper we aim to establish some results depending on the comparative growth properties of composite transcendental entire or meromorphic functions and some special type of differential polynomials generated by one of the factors on the basis of generalized order α,β and generalized lower order α,β where α and β are continuous non-negative functions defined on −∞,+∞.