In the present paper, making use of the operator D-p(delta)(lambda, mu,l), two new subclasses S-lambda,mu,l(delta)(A, B; sigma,p) and ST lambda,mu,l delta(A, B; sigma,p) of p-valent functions are investigated in the open unit disk. Some interesting relations and characteristics such as inclusion relationships, neighborhoods, partial sums and some applications of fractional calculus of functions belonging to each of these subclasses S-lambda,mu,l(delta)(A, B; sigma,p) and ST lambda,mu,l delta(A, B; sigma,p) are investigated. Relevant connections of the definitions and results presented in this paper with those obtained in several earlier works on the subject are also pointed out.