  Many authors have considered and investigated generalized fractional
differential operators. The main object of this present paper is to define a
new generalized fractional differential operator
$\mathfrak{T}^{\beta,\tau,\gamma},$ which generalized the Srivastava-Owa
operators. Moreover, we investigate of the geometric properties such as
univalency, starlikeness, convexity for their normalization. Further,
boundedness and compactness in some well known spaces, such as Bloch space for
last mention operator also are considered. Our tool is based on the generalized
hypergeometric function.
