The authors introduced and addressed  several new subclasses  of the family of meromorphically multivalent -star-like functions in the punctured unit disk  in this study, which makes use of several higher order -derivatives. Many fascinating properties and characteristics are extracted systematically for each of these newly identified function classes. Distortion theorems and radius problems are among these characteristics and functions. A number of coefficient inequalities for functions belonging to the subclasses are studied, and discussed, as well as a suitable condition for them is set. The numerous results are presented in this study and the previous works on this

      In this paper, we define a new subclass of multivalent functions defined by the generalized integral operator with negative coefficients in the open unit disk U. We also give and study some interesting properties such as coefficient estimates, subordination theorems and integral means inequalities by using the famous Littlewood's subordination theorem. Finally, we conclude a type of inequalities that is upper bound and lower bound for topology multivalent functions of all analytic functions.  

We presented in this paper a new class containing analytic univalent functions defined on unit disk. We obtained many geometric properties , like , coefficient inequality , distortion and growth theorems, convolution property, convex set, arithmetic mean and radius of starlikness and convexity by using Gaussian hypergeometric function for the class

      In this paper, we consider new subclasses     of meromorphic uniformly of multivalent functions in    with fixed second coefficient, we obtain the estimation of coefficients, distortion theorems, closure theorems and some other results.

The main goal of this paper is to study applications of the fractional calculus techniques for a certain subclass of multivalent analytic functions on Hilbert Space. Also, we obtain the coefficient estimates, extreme points, convex combination and hadamard product.

       In the present paper, by making use of the new generalized operator, some results of third order differential subordination and differential superordination consequence for analytic functions are obtained. Also, some sandwich-type theorems are presented.

In this paper, making use of the q-R uscheweyh differential  operator , and  the  notion of t h e J anowski f unction, we study some subclasses of  holomorphic   f- unction s . Moreover , we obtain so me geometric characterization like co efficient es timat es , rad ii of starlikeness ,distortion theorem , close- t o- convexity , con vexity, ext reme point s, neighborhoods, and the i nte gral mean inequalities of func tions affiliation to these c lasses

     This work is devoted to define new generalized gamma and beta functions involving the recently suggested seven-parameter Mittag-Leffler function, followed by a review of all related special cases. In addition, necessary investigations are affirmed for the new generalized beta function, including, Mellin transform, differential formulas, integral representations, and essential summation relations. Furthermore, crucial statistical application has been realized for the new generalized beta function.  

     This work is devoted to define new generalized gamma and beta functions involving the recently suggested seven-parameter Mittag-Leffler function, followed by a review of all related special cases. In addition, necessary investigations are affirmed for the new generalized beta function, including, Mellin transform, differential formulas, integral representations, and essential summation relations. Furthermore, crucial statistical application has been realized for the new generalized beta function.  

     In this paper, we introduce and discuss an extended subclass〖 Ą〗_p^*(λ,α,γ) of meromorphic multivalent functions involving Ruscheweyh derivative operator. Coefficients inequality, distortion theorems, closure theorem for this subclass are obtained.