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

Boundedness of normalization generalized differential operator of fractional formal