Aust. J. Math. Anal. Appl. Vol. 18 (2021), No. 1, Art. 6, 9 pp. AJMAA SOME PROPERTIES ON A CLASS OF p-VALENT FUNCTIONS INVOLVING GENERALIZED DIFFERENTIAL OPERATOR ABDELJABBAR TALAL YOUSEF 1 , ZABIDIN SALLEH 2,* AND TARIQ AL-HAWARY 3 Received 3 April, 2020; accepted 27 December, 2020; published 12 February, 2021. 1,2 DEPARTMENT OF MATHEMATICS,FACULTY OF OCEAN ENGINEERING TECHNOLOGY AND I NFORMATICS, UNIVERSITI MALAYSIA TERENGGANU, 21030 KUALA NERUS,TERENGGANU,MALAYSIA. abduljabaryousef@gmail.com 1 , zabidin@umt.edu.my 2 3 DEPARTMENT OF APPLIED SCIENCE,AJLOUN COLLEGE,AL-BALQA APPLIED UNIVERSITY,AJLOUN 26816, J ORDAN. tariq_amh@yahoo.com 3 ABSTRACT. This paper aiming to introduce a new differential operator T m w,p,α,β,λ,δ in the open unit disc U = {z ∈ C : |z| < 1}. We then, introduce a new subclass of analytic function G w m (μ, λ, α, β, δ, b, p). Moreover, we discuss coefficient estimates, growth and distortion theo- rems, and inclusion properties for the functions belonging to the class G w m (μ, λ, α, β, δ, b, p). Key words and phrases: Analytic functions; p-valent functions; Generalized differential operator. 2010 Mathematics Subject Classification. Primary 30C45, 30C50. ISSN (electronic): 1449-5910 c  2021 Austral Internet Publishing. All rights reserved.