Some relations involving a generalized fractional derivative operator

ON GENERALIZED k-FRACTIONAL DERIVATIVE OPERATOR

The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to khypergeometric and k-Appell’s functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and Wright hypergeometric functions.

Some Relations between Certain Classes of Analytic Multivalent Functions Involving Generalized Sălăgean Operator

Abstract: The aim of this paper is to introduce and study two subclasses of multivalent functions involving generalized Sălăgean operator. Our classes M m,σ p,n (γ;η) and N m,σ p,n (α ,β ;η) unify the standard classes of multivalent starlike functions of order η , multivalent convex functions of order η , and Bazilević functions. Some connections between our classes are obtained and several con...

Some relations between ε-directional derivative and ε-generalized weak subdifferential

In this paper, we study ε-generalized weak s...

On Differential Subordinations of Multivalent Functions Involving a Certain Fractional Derivative Operator

On certain fractional calculus operators involving generalized Mittag-Leffler function

The object of this paper is to establish certain generalized fractional integration and differentiation involving generalized Mittag-Leffler function defined by Salim and Faraj [25]. The considered generalized fractional calculus operators contain the Appell's function $F_3$ [2, p.224] as kernel and are introduced by Saigo and Maeda [23]. The Marichev-Saigo-Maeda fractional calculus operators a...